1. (2 points)Two random samples are selected from two indepe.docx

1. (2 points)
Two random samples are selected from two independent pop-
ulations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
n1 = 37, x̄ 1 = 52.4, s1 = 5.8
n2 = 48, x̄ 2 = 75, s2 = 10
Find a 92.5% confidence interval for the difference µ1− µ2
of the means, assuming equal population variances.
Confidence Interval =
Answer(s) submitted:
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2. (2 points) In order to compare the means of two popu-
lations, independent random samples of 238 observations are
selected from each population, with the following results:
Sample 1 Sample 2
x1 = 1 x2 = 3
s1 = 120 s2 = 200
(a) Use a 97 % confidence interval to estimate the difference
between the population means (µ1−µ2).
≤ (µ1−µ2)≤

(b) Test the null hypothesis: H0 : (µ1− µ2) = 0 versus the al-
ternative hypothesis: Ha : (µ1− µ2) 6= 0. Using α = 0.03, give
the following:
(i) the test statistic z =
(ii) the positive critical z score
(iii) the negative critical z score
The final conclustion is
• A. We can reject the null hypothesis that (µ1−µ2) = 0
and accept that (µ1−µ2) 6= 0.
• B. There is not sufficient evidence to reject the null hy-
pothesis that (µ1−µ2) = 0.
(c) Test the null hypothesis: H0 : (µ1−µ2) = 26 versus the al-
ternative hypothesis: Ha : (µ1−µ2) 6= 26. Using α = 0.03, give
the following:
(i) the test statistic z =
(ii) the positive critical z score
(iii) the negative critical z score
• A. We can reject the null hypothesis that (µ1−µ2) = 26
and accept that (µ1−µ2) 6= 26.
pothesis that (µ1−µ2) = 26.
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3. (2 points) Two independent samples have been selected,
70 observations from population 1 and 83 observations from
population 2. The sample means have been calculated to be
x1 = 14.9 and x2 = 10.5. From previous experience with these
populations, it is known that the variances are σ21 = 20 and
σ22 = 21.
(a) Find σ(x1−x2).
answer:
(b) Determine the rejection region for the test of H0 :
(µ1−µ2) = 2.92 and Ha : (µ1−µ2)> 2.92 Use α = 0.05.
z >
(c) Compute the test statistic.
z =
• A. We can reject the null hypothesis that (µ1− µ2) =
2.92 and accept that (µ1−µ2)> 2.92.
pothesis that (µ1−µ2) = 2.92.
(d) Construct a 95 % confidence interval for (µ1−µ2).
≤ (µ1−µ2)≤

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4. (2 points) Randomly selected 100 student cars have ages
with a mean of 7.2 years and a standard deviation of 3.4 years,
while randomly selected 85 faculty cars have ages with a mean
of 5.4 years and a standard deviation of 3.3 years.
1
1. Use a 0.01 significance level to test the claim that student
cars are older than faculty cars.
The test statistic is
The critical value is
Is there sufficient evidence to support the claim that student
cars are older than faculty cars?
• A. Yes
• B. No
2. Construct a 99% confidence interval estimate of the dif-
ference µ1−µ2, where µ1 is the mean age of student cars and µ2
is the mean age of faculty cars.

< (µ1−µ2)<
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5. (2 points) Randomly selected 15 student cars have ages
with a mean of 7.9 years and a standard deviation of 3.4 years,
while randomly selected 14 faculty cars have ages with a mean
of 5.5 years and a standard deviation of 3.3 years.
1. Use a 0.05 significance level to test the claim that student
cars are older than faculty cars.
(a) The test statistic is
(b) The critical value is
(c) Is there sufficient evidence to support the claim that stu-
dent cars are older than faculty cars?
• A. Yes
• B. No
2. Construct a 95% confidence interval estimate of the dif-
ference µs−µ f , where µs is the mean age of student cars and µ
f
is the mean age of faculty cars.
< (µs−µ f )<
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7. (2 points) In which of the following scenarios will con-
ducting a two-sample t-test for means be appropriate? CHECK
ALL THAT APPLY.
• A. To test if the proportion of low-income families
is higher than that of high-income families in British
Columbia.
• B. To test if there is a difference between the mean an-
nual income of husbands and that of wives in Canada.
• C. To test if the mean annual income of Ontarians is
higher than that of British Columbians.
• D. To test if there is a difference between the propor-
tion of low-income families in British Columbia and a
known national proportion.
• E. To test if there is a difference between the mean
annual income of male British Columbians and that of
female British Columbians.
• F. To test if there is a difference between the mean
annual income of British Columbians and a known na-
tional mean.
• G. None of the above
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Mathematical Association of America
2
1. (2 points) Golf-course designers have become concerned
that old courses are becoming obsolete since new technology
has given golfers the ability to hit the ball so far. Designers,
therefore, have proposed that new golf courses need to be built
expecting that the average golfer can hit the ball more than 230
yards on average. Suppose a random sample of 195 golfers be
chosen so that their mean driving distance is 229.3 yards. The
population standard deviation is 46.9. Use a 5% significance
level.
Calculate the followings for a hypothesis test where H0 : µ =
230 and H1 : µ < 230 :
(a) The test statistic is
(b) The P-Value is
• A. There is not sufficient evidence to warrant rejection
of the claim that the mean driving distance is equal to
230
• B. There is sufficient evidence to warrant rejection of
the claim that the mean driving distance is equal to 230

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2. (2 points) Given the significance level α = 0.05 find the
following:
(a) left-tailed z value
z =
(b) right-tailed z value
z =
(c) two-tailed z value
|z|=
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3. (2 points) It is necessary for an automobile producer to
estimate the number of miles per gallon achieved by its cars.
Suppose that the sample mean for a random sample of 130 cars
is 28 miles and assume the standard deviation is 2 miles. Now
suppose the car producer wants to test the hypothesis that µ, the
mean number of miles per gallon, is 28.1 against the alternative
hypothesis that it is not 28.1. Conduct a test using α = .05 by
giving the following:

(a) positive critical z score
(b) negative critical z score
(c) test statistic
• A. We can reject the null hypothesis that µ = 28.1 and
accept that µ 6= 28.1.
pothesis that µ = 28.1.
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4. (2 points) A new cream that advertises that it can reduce
wrinkles and improve skin was subject to a recent study. A sam-
ple of 50 women over the age of 50 used the new cream for 6
months. Of those 50 women, 38 of them reported skin improve-
ment(as judged by a dermatologist). Is this evidence that the
cream will improve the skin of more than 60% of women over
the age of 50? Test using α = 0.05.
(a) Test statistic: z =
(b) Critical Value: z∗ =
(c) The final conclusion is
• A. We can reject the null hypothesis that p = 0.6 and
accept that p > 0.6. That is, the cream can improve the
skin of more than 60% of women over 50.

pothesis that p = 0.6. That is, there is not sufficient
evidence to reject that the cream can improve the skin
of more than 60% of women over 50.
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5. (2 points) The contents of 40 cans of Coke have a mean of
x = 12.15. Assume the contents of cans of Coke have a normal
distribution with standard deviation of σ = 0.1. Find the value
of the test statistic z for the claim that the population mean is
µ = 12.
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6. (2 points) The contents of 34 cans of Coke have a mean of
x = 12.15 and a standard deviation of s = 0.11. Find the value
of the test statistic t for the claim that the population mean is
µ = 12.

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7. (2 points) Test the claim that for the population of statistics
final exams, the mean score is 71 using alternative hypothesis
that the mean score is different from 71. Sample statistics in-
clude n = 20, x = 72, and s = 14. Use a significance level of
α = 0.05. (Assume normally distributed population.)
The positive critical value is
The negative critical value is
The conclusion is
• A. There is not sufficient evidence to reject the claim
that the mean score is equal to 71.
• B. There is sufficient evidence to reject the claim that
the mean score is equal to 71.
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8. (2 points) The one-sample t statistic for a test of
H0 : µ = 15
Ha : µ < 15

based on n = 5 observations has the value t = -1.248.
(a) What are the degrees of freedom for this statistic?
(b) Between what two probabilities P from a t-table does the
P-value of this statistic fall?
(State the smaller probability in the left box.) to
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9. (2 points) Andrew thinks that people living in a rural envi-
ronment have a healthier lifestyle than other people. He
believes
the average lifespan in the USA is 77 years. A random sample
of 18 obituaries from newspapers from rural towns in Idaho give
x̄ = 79.38 and s = 2.39. Does this sample provide evidence that
people living in rural Idaho communities live longer than 77
years?
(a) State the null and alternative hypotheses: (Type ”mu” for
the symbol µ , e.g. mu >1 for the mean is greater than 1, mu
< 1 for the mean is less than 1, mu not = 1 for the mean is not
equal to 1)
H0 :
Ha :
(b) Find the test statistic, t =
(c) Answer the question: Does this sample provide evidence
that people living in rural Idaho communities live longer than

77 years? (Use a 10
(Type: Yes or No)
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10. (2 points) The sample mean and standard deviation from
a random sample of 22 observations from a normal population
were computed as x̄ = 29 and s = 12. Calculate the t statistic of
the test required to determine whether there is enough evidence
to infer at the 8% significance level that the population mean is
greater than 27.
Test Statistic =
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11. (2 points) A recent poll of 2500 randomly selected 18-25-
year-olds revealed that 290 currently use marijuana or hashish.
According to a publication, 12.6 % of 18-25-year-olds were cur-
rent users of marijuana or hashish in 1997. Do the data provide
sufficient evidence to conclude that the percentage of 18-25-
year-olds who currently use marijuana or hashish has changed
from the 1997 percentage of 12.6%? Use α = 0.05 significance
level.
test statistic z =
positive critical z score

negative critical z score
The final conclusion is
• A. There is not sufficient evidence to conclude that the
percentage of 18-25-year-olds who currently use mari-
juana or hashish has changed from the 1997 percentage
of 12.6%.
2
• B. There is sufficient evidence to conclude that the
percentage of 18-25-year-olds who currently use mari-
juana or hashish has changed from the 1997 percentage
of 12.6%.
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12. (2 points) Physicians at a clinic gave what they thought
were drugs to 840 patients. Although the doctors later learned
that the drugs were really placebos, 58 % of the patients re-
ported an improved condition. Assume that if the placebo is
ineffective, the probability of a patients condition improving is
0.57. Test the hypotheses that the proportion of patients im-
proving is > 0.57.
Find the test statistics:

z =
Find the p-value.
p =
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13. (2 points) A survey of 1850 people who took trips re-
vealed that 200 of them included a visit to a theme park. Based
on those survery results, a management consultant claims that
less than 12 % of trips include a theme park visit. Test this
claim
using the α = 0.05 significance level.
The critical value is
The conclusion is
• A. There is sufficient evidence to support the claim that
less than 12 % of trips include a theme park visit.
• B. There is not sufficient evidence to support the claim
that less than 12 % of trips include a theme park visit.
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14. (2 points) Albert thinks that he has a special relationship
with the number 6. In particular, Albert thinks that he would
roll a 6 with a fair 6-sided die more often than you’d expect
by chance alone. Suppose p is the true proportion of the time
Albert will roll a 6.
(a) State the null and alternative hypotheses for testing Al-
bert’s claim. (Type the symbol ”p” for the population propor-
tion, whichever symbols you need of ”¡”, ”¿”, ”=”, ”not =” and
express any values as a fraction e.g. p = 1/3)
H0 =
Ha =
(b) Now suppose Albert makes n = 46 rolls, and a 6 comes up
10 times out of the 46 rolls. Determine the P-value of the test:
P-value =
(c) Answer the question: Does this sample provide evidence
at the 5 percent level that Albert rolls a 6 more often than you’d
expect?
(Type: Yes or No)
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15. (2 points) According to a recent marketing campaign,
130 drinkers of either Diet Coke or Diet Pepsi participated
in a blind taste test to see which of the drinks was their fa-
vorite. In one Pepsi television commercial, an anouncer states

that ”in recent blind taste tests, more than one half of the sur-
veyed preferred Diet Pepsi over Diet Coke.” Suppose that out of
those 130, 54 preferred Diet Pepsi. Test the hypothesis, using
α = 0.01 that more than half of all participants will select Diet
Pepsi in a blind taste test by giving the following:
(a) the test statistic
(b) the critical z score
• A. We can reject the null hypothesis that p ≤ 0.5 and
accept that p > 0.5.
pothesis that p≤ 0.5.
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3
1. (2 points) Is the following statement true, or false? An-
swer using the pull down menu.
? 1. As a general rule, the normal distribution is used to ap-
proximate the sampling distribution of the sample pro-

portion only if the expected successes and failures are
10: np ≥ 10,n(1− p)≥ 10.
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2. (2 points) Is the following statement true, or false? An-
swer using the pull down menu.
? 1. As a general rule, the normal distribution is used to ap-
proximate the sampling distribution of the sample pro-
portion only if the sample size n is greater than or equal
to 30.
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3. (2 points) A report says that 82% of British Columbians
over the age of 25 are high school graduates. A survey of ran-
domly selected residents of a certain city included 1290 who
were over the age of 25, and 1012 of them were high school
graduates.
Part a
Which of the following gives the approximated model for the
sample proportion of high school graduates in a sample of 1290
students?
Answer:
• Select one

• N(0.78,0.011)
• N(0.82,0.011)
• N(78,1.11)
• N(82,1.11)
• N(1012, 13.80)
Part b
How many standard deviation away is the sample proportion of
high school graduates (1012/1290) is away from the mean? You
will need to use the correct approximated model to answer the
question.
Answer:
• Select one
• Less than -2
• Between -2 and -1
• Between -1 and 1
• Between 1 and 2
• More than 2
Part c
Is the city’s result of 1012 unusually high, low, or neither? You
will need to use the correct approximated model to answer the
question.
Answer: [Select one/High/Low/Neither]
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4. (2 points) A study claims that 75% of children under the
age of 13 in British Columbia have been vaccinated from the

chicken pox. A survey of randomly selected residents of a cer-
tain city included 650 children who were under the age of 13,
and 197 of them were not vaccinated.
Part a
What is the approximated probability that sample proportion
of non-vaccinated children in a sample of 650 children is more
than 197/650? (Please carry answers to at least six decimal
places in intermediate steps. Give your final answer to the near-
est three decimal places).
Part b
Is the number of non-vaccinated children in this city sample
unusually high, low, or neither?
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5. (2 points) Rock band The Rolling Stones have played
scores of concerts in the last twenty years. For 30 randomly se-
lected Rolling Stones concerts, the mean gross earnings is 2.73
million dollars.
Part a) Assuming a population standard deviation gross
earnings of 0.51 million dollars, obtain a 99% confidence inter-
val for the mean gross earnings of all Rolling Stones concerts
1

(in millions). Please carry at least three decimal places in in-
termediate steps. Give your answer to the nearest 3 decimal
places.
Confidence interval: ( , ).
Part b)
Which of the following is the correct interpretation for your
answer in part (a)?
• A. We can be 99% confident that the mean gross earn-
ings for this sample of 30 Rolling Stones concerts lies
in the interval
• B. If we repeat the study many times, 99% of the calcu-
lated confidence intervals will contain the mean gross
earning of all Rolling Stones concerts.
• C. There is a 99% chance that the mean gross earnings
of all Rolling Stones concerts lies in the interval
• D. None of the above
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6. (2 points) A random sample of n measurements was se-
lected from a population with standard deviation σ = 17.4 and
unknown mean µ. Calculate a 90 % confidence interval for µ for
each of the following situations:

(a) n = 40, x = 104.3
≤ µ ≤
(b) n = 65, x = 104.3
≤ µ ≤
(c) n = 95, x = 104.3
≤ µ ≤
(d) In general, we can say that for the same confidence
level, increasing the sample size the margin of er-
ror (width) of the confidence interval. (Enter: ”DECREASES”,
”DOES NOT CHANGE” or ”INCREASES”, without the
quotes.)
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7. (2 points) A random sample of 120 observations produced
a mean of x = 23.1 from a population with a normal distribution
and a standard deviation σ = 2.13.
(a) Find a 90% confidence interval for µ
≤ µ ≤
(b) Find a 95% confidence interval for µ
≤ µ ≤

(c) Find a 99% confidence interval for µ
≤ µ ≤
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8. (2 points) An online used car company sells second-hand
cars. For 30 randomly selected transactions, the mean price is
2800 dollars.
Part a) Assuming a population standard deviation transac-
tion prices of 180 dollars, obtain a 99% confidence interval for
the mean price of all transactions. Please carry at least three
decimal places in intermediate steps. Give your final answer to
the nearest two decimal places.
Confidence interval: ( , ).
Part b)
Which of the following is the correct interpretation for your
answer in part (a)?
• A. There is a 99% chance that the mean price of all
transactions lies in the interval
• B. If we repeat the study many times, 99% of the cal-

culated confidence intervals will contain the mean price
of all transactions.
• C. We can be 99% confident that the mean price for this
sample of 30 transactions lies in the interval
• D. None of the above
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9. (2 points)
Use the given data to find the 95% confidence interval esti-
mate of the population mean µ. Assume that the population has
a normal distribution.
IQ scores of professional athletes:
Sample size n = 25
Mean x = 104
Standard deviation s = 10
2
< µ <
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10. (2 points) A random sample of 19 size AA batteries for
toys yield a mean of 2.67 hours with standard deviation, 1.31
hours.
(a) Find the critical value, t*, for a 99% CI. t* =
(b) Find the margin of error for a 99% CI.
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Select True or False from each pull-down menu, depending
on whether the corresponding statement is true or false.
? 1. If a sample of size 250 is selected, the value of A for the
probability P(−A ≤ t ≤ A) = 0.90 is 1.651.
? 2. If a sample has 18 observations and a 90% confidence
estimate for µ is needed, the appropriate t-score is
1.740.
? 3. If a sample has 15 observations and a 95% confidence
estimate for µ is needed, the appropriate t-score is
1.753.
? 4. If a sample of size 20 is selected, the value of A for the
probability P(t ≥ A) = 0.01 is 2.528.
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12. (2 points) A government official is in charge of allocat-
ing social programs throughout the city of Vancouver. He will
decide where these social outreach programs should be located
based on the percentage of residents living below the poverty
line in each region of the city. He takes a simple random sam-
ple of 121 people living in Gastown and finds that 25 have an
annual income that is below the poverty line.
Part i) The proportion of the 121 people who are living
below the poverty line, 25/121, is a:
• A. statistic.
• B. parameter.
• C. variable of interest.
Part ii) Use the sample data to compute a 95% confidence
interval for the true proportion of Gastown residents living be-
low the poverty line.
(Please carry answers to at least six decimal places in in-
termediate steps. Give your final answer to the nearest three
decimal places).
95% confidence interval = ( , )
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13. (2 points) Refer to the following scenario.
A government official is in charge of allocating social pro-
grams throughout the city of Vancouver. He will decide where
these social outreach programs should be located based on the
percentage of residents living below the poverty line in each re-
gion of the city. He takes a simple random sample of 127 people
living in Gastown and finds that 25 have an annual income that
is below the poverty line.
Suppose that the government official wants to re-estimate the
population proportion and wishes for his 95% confidence inter-
val to have a margin of error no larger than 0.05. How large a
sample should he take to achieve this? Please carry answers to
at least six decimal places in intermediate steps.
Sample size =
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14. (2 points) A poll is taken in which 348 out of 600 ran-
domly selected voters indicated their preference for a certain
candidate.
(a) Find a 99% confidence interval for p.
≤ p ≤
(b) Find the margin of error for this 99% confidence interval
for p.
(c) Without doing any calculations, indicate whether the mar-
gin of error is larger or smaller or the same for an 80% confi-

dence interval.
• A. larger
• B. smaller
• C. same
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15. (2 points) A random sample of 1600 car owners in a par-
ticular city found 544 car owners who received a speeding
ticket
this year. Find a 95% confidence interval for the true percent of
car owners in this city who received a speeding ticket this year.
Express your results to the nearest hundredth of a percent.
Answer: to %
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4
1. (2 points) In a very large population, the distribution of
annual income is skewed, with a long right tail. We take a sim-
ple random sample of n people from this population and record
the n incomes. We expect a histogram of the n incomes in the
sample
• A. will resemble a Uniform distribution for all values
of n.
• B. will resemble a Uniform distribution provided n is
large.
• C. will not resemble a Normal distribution whatever the
value of n.
• D. will resemble a Normal distribution for all values of
n.
• E. will resemble a Normal distribution provided n is
large.
•
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2. (2 points) For the following problems, select the best re-
sponse:
(a) Sampling variation is caused by

• A. changes in a population parameter that cannot be
predicted.
• B. systematic errors in our procedure.
• C. random selection of a sample.
• D. changes in a population parameter from sample to
sample.
(b) A statistic is said to be unbiased if
• A. the survey used to obtain the statistic was designed
so as to avoid even the hint of racial or sexual prejudice.
• B. the mean of its sampling distribution is equal to the
true value of the parameter being estimated.
• C. both the person who calculated the statistic and the
subjects whose responses make up the statistic were
truthful.
• D. it is used for only honest purposes.
(c) The sampling distribution of a statistic is
• A. the probability that we obtain the statistic in repeated
random samples.
• B. the distribution of values taken by a statistic in all
possible samples of the same size from the same popu-
lation.
• C. the mechanism that determines whether or not ran-
domization was effective.
• D. the extent to which the sample results differ system-

atically from the truth.
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•
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3. (2 points) The following table provides the starting players
of a basketball team and their heights
Player A B C D E
Height (in.) 75 77 79 82 85
a. The population mean height of the five players is .
b. Find the sample means for samples of size 2.
A, B: x̄ = .
A, C: x̄ = .
A, D: x̄ = .
A, E: x̄ = .
B, C: x̄ = .
B, D: x̄ = .
B, E: x̄ = .
C, D: x̄ = .
C, E: x̄ = .
D, E: x̄ = .
c. Find the mean of all sample means from above:
x̄ = .
The answers from parts (a) and (c)
• A. should always be equal

• B. are not equal
• C. if they are equal it is only a coincidence.
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4. (2 points)
What effect does the sample size have on the standard devi-
ation of all possible sample means?
• A. It gets smaller as the sample size grows.
• B. The sample size has no effect on it.
• C. It gets larger as the sample size grows.
•

(incorrect)
5. (2 points)
Explain why increasing the sample size tends to result in a
smaller sampling error when a sample mean is used to estimate
a population mean.
• A. The above statement is incorrect, the sample size has
no effect on the sampling error.
• B. The larger the sample size, the more closely the pos-
sible values of x̄ cluster around the mean of x̄
• C. If the sample size is larger, the possible values of x̄
are farther from the mean of x̄
•
(incorrect)
6. (2 points) The scores of students on the SAT college en-
trance examinations at a certain high school had a normal distri-
bution with mean µ = 541.2 and standard deviation σ = 28.4.
(a) What is the probability that a single student randomly
chosen from all those taking the test scores 545 or higher?
ANSWER:
For parts (b) through (d), consider a simple random sample
(SRS) of 35 students who took the test.
(b) What are the mean and standard deviation of the sample
mean score x̄ , of 35 students?

The mean of the sampling distribution for x̄ is:
The standard deviation of the sampling distribution for x̄ is:
(c) What z-score corresponds to the mean score x̄ of 545?
ANSWER:
(d) What is the probability that the mean score x̄ of these
students is 545 or higher?
ANSWER:
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(incorrect)
7. (2 points)
A study on the length of time a person brushes their teeth is
conducted on a large population of adults. The mean brushing
time is µ and the standard deviation is σ. A simple random sam-
ple of 100 adults is considered.
(NOTE: For the following problems enter: ” GREATER
THAN ”, ” EQUAL TO ”, ” LESS THAN ”, or ” NOT
ENOUGH INFORMATION ”, without the quotes.)
(a) The mean of the sampling distribution is the
mean of the population.
(b) The standard deviation of the sampling distribution is
the standard deviation of the population.

•
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(incorrect)
8. (2 points) Assume that women’s weights are normally
distributed with a mean given by µ = 143 lb and a standard
deviation given by σ = 29 lb.
(a) If 1 woman is randomly selected, find the probabity that
her weight is between 108 lb and 175 lb
(b) If 3 women are randomly selected, find the probability
that they have a mean weight between 108 lb and 175 lb
(c) If 64 women are randomly selected, find the probability
that they have a mean weight between 108 lb and 175 lb
•
•
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(incorrect)
9. (2 points) A sample of n = 11 observations is drawn from
a normal population with µ = 940 and σ = 190. Find each of
the following:
A. P(X
̄ > 1031)
Probability =
B. P(X
̄ < 836)
Probability =
C. P(X
̄ > 871)
Probability =

•
2
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(incorrect)
10. (2 points)
A sample of 12 measurements has a mean of 39 and a stan-
dard deviation of 4. Suppose that the sample is enlarged to 14
measurements, by including two additional measurements hav-
ing a common value of 39 each.
A. Find the mean of the sample of 14 measurements.
Mean =
B. Find the standard deviation of the sample of 14 measure-
ments.
Standard Deviation =
•
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(incorrect)

3
1. (2 points) Which of the following are true about all normal
distributions? Check all that apply
• A. They have one large tail.
• B. They are bimodal.
• C. They have no major outliers.
• D. They are categorically sharp.
The z-score corresponding to an observed value of a variable
tells you the number of standard deviations that the observation
is from the mean
• A. True
• B. False
A positive z-score indicates that the observation is
• A. above the mean
• B. below the mean
•
•
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(incorrect)
2. (2 points) a) Fact: the region under the standard normal
curve that lies to the left of −1.95 has area 0.0255881.
Without consulting a table or a calculator giving areas under
the standard normal curve, determine the area under the stan-

dard normal curve that lies to the right of 1.95.
answer:
b) Which property of the standard normal curve allowed you
to answer part a)?
• A. The total area under the curve is 1
• B. Almost all the area under the standard normal curve
lies between −3 and 3
• C. The standard normal curve is symmetric about 0
• D. The standard normal curve extends indefinitely in
both directions
• E. None of the above
•
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(incorrect)
3. (2 points) What are the parameters for a normal curve?
• A. the sample mean and sample standard deviation
• B. the population mean and population variance
• C. the population mean and population standard devia-
tion
• D. the population median and population standard de-
viation
•

(incorrect)
4. (2 points) Which of the following normal distributions has
the widest spread?
• A. A normal distribution with mean 0 and standard de-
viation 2
• B. A normal distribution with mean 2 and standard de-
viation 1
• C. A normal distribution with mean 1 and standard de-
viation 3
• D. A normal distribution with mean 3 and standard de-
viation 2
•
(incorrect)
5. (2 points) Consider two normal distributions, one with
mean −19 and standard deviation 11, the other with mean 6 and
standard deviation 11. Answer the following statements using
true or false.
a) The two distributions have the same shape.
answer:
b) The two distributions are centered at the same place.
answer:

•
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(incorrect)
1
6. (2 points) The U.S. Bureau of the Census conducts nation-
wide sureys on characteristics of U.S. households.
Household size Relative Frequency
1 0.1
2 0.05
3 0.275
4 0.25
5 0.125
6 0.175
7 0.025
Total 1
a) Use the previous relative frequency distribution to obtain
the percentage of U.S. households that are between sizes 3 and
5.
answer:
b) Use your answer from part a) to estimate the area under
the corresponding normal curve that lies between 3 and 5.
answer:
•

•
(incorrect)
7. (2 points) Length of skateboards in a skateshop are nor-
mally distributed with a mean of 32 in and a standard deviation
of 0.6 in. The figure below shows the distribution of the length
of skateboards in a skateshop. Calculate the shaded area under
the curve. Express your answer in decimal form with at least
two decimal place accuracy.
Answer:
•
(incorrect)
8. (2 points) Find the following probabilities for the standard
normal random variable z:
(a) P(−1.83 ≤ z ≤ 0.78) =
(b) P(−0.8 ≤ z ≤ 0.37) =
(c) P(z ≤ 0.71) =
(d) P(z >−1.16) =
•
•
•
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(incorrect)

10. (2 points) Select True or False from each pull-down
menu, depending on whether the corresponding statement is
true or false.
? 1. Using the standard normal curve, the z−score repre-
senting the 10th percentile is 1.28.
? 2. A random variable X is normally distributed with a
mean of 150 and a variance of 36. Given that X = 120,
its corresponding z− score is 5.0
? 3. The mean and standard deviation of an exponential ran-
dom variable are equal to each other.
? 4. The mean and standard deviation of a normally dis-
tributed random variable which has been standardized
are one and zero, respectively.
•
•
•
•
(incorrect)
11. (2 points) Suppose that X is normally distributed with
mean 95 and standard deviation 28.
A. What is the probability that X is greater than 147.08?
Probability =
B. What value of X does only the top 15% exceed?
X =

•
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(incorrect)
13. (2 points) Suppose a car manufacturer believes its wind-
screen wipers will last on average for three years on their cars if
driven by a typical driver in the province. Moreover, the manu-
facturer believes the lifetime of the wipers under such
conditions
is Normally distributed with a standard deviation of two years.
Find the probability that, if on a car driven by a typical driver, a
windscreen wiper lasts for a time that is not within 1.5 years of
the mean lifetime.
The probability is:
•
(incorrect)
2
14. (2 points) An exam consists of 42 multiple-choice ques-
tions. Each question has a choice of five answers, only one of
which is correct. For each correct answer, a candidate gets 1
mark, and no penalty is applied for getting an incorrect answer.
A particular candidate answers each question purely by guess-
work.
Using Normal approximation to Binomial distribution with
continuity correction, what is the estimated probability this stu-

dent obtains a score greater than or equal to 10? Please use
R to obtain probabilities and keep at least 6 decimal places in
intermediate steps.
• A. 0.4059
• B. 0.2089
• C. 0.6643
• D. 0.5650
• E. 0.3357
•
(incorrect)
15. (2 points) The shelf life of a battery produced by one ma-
jor company is known to be Normally distributed, with a mean
life of 4 years and a standard deviation of 0.6 years.
What value of shelf life do 16% of the battery shelf lives fall
above? Round your answer to one decimal place.
Answer: years.
•
(incorrect)
16. (2 points) Cans of regular Coke are labeled as containing
12 oz.
Statistics students weighed the contents of 10 randomly chosen
cans, and found the mean weight to be 12.11 ounces.
Assume that cans of Coke are filled so that the actual amounts
are normally distributed with a mean of 12.00 oz and a standard

deviation of 0.11 oz. Find the probability that a sample of 10
cans will have a mean amount of at least 12.11 oz.
•
(incorrect)
17. (2 points) Assume that the readings on the thermometers
are normally idstributed with a mean of 0◦ and a standard devi-
ation of 1.00◦C.
Find P60, the 60th percentile.
This is the temperature reading separating the bottom 60 %
from the top 40 %.
•
(incorrect)
18. (2 points) Healty people have body temperatures that
are normally distributed with a mean of 98.20◦F and a standard
deviation of 0.62◦F .
(a) If a healthy person is randomly selected, what is the
probability that he or she has a temperature above 99.6◦F?
answer:
(b) A hospital wants to select a minimum temperature for
requiring further medical tests. What should that temperature
be, if we want only 1 % of healty people to exceed it?

answer:
•
•
(incorrect)
3
1. (2 points) Find the expected value for the random variable:
X
2
4
5
7
P(X)
0.2
0.14
0.14
0.52
E(X) =
•
(incorrect)

2. (2 points) A raffle has a grand prize of a Caribbean cruise
valued at $6000 with a second prize of a Rocky Point vacation
valued at $1300. If each ticket costs $2 and 8600 tickets are
sold, what are the expected winnings far a ticket buyer? Ex-
press to at least three decimal place accuracy in dollar form
(as opposed to cents).
Answer: $
•
(incorrect)
4. (2 points)
Find the mean, variance and standard deviation for the prob-
ability distribution given below:
X -1 2 8 10
P(X) 0.584 0.127 0.206 0.083
A. Mean =
B. Variance =
C. Standard Deviation =
•
•
•
(incorrect)
5. (2 points) A poll of 64 students found that 49% were in
favor of raising tution to build a new football stadium. The
stan-

dard deviation of this poll is 8%. What would be the standard
deviation if the sample size were increased from 64 to 245?
Answer: %
•
(incorrect)
6. (2 points) A study claims that 75% of children under the
age of 13 in British Columbia have been vaccinated from the
chicken pox. A survey of randomly selected residents of a cer-
tain city included 650 children who were under the age of 13,
and 197 of them were not vaccinated.
Is the number of non-vaccinated children in this city sample un-
usually high, low, or neither?
•
(incorrect)
7. (2 points) Suppose that you flip a coin 11 times. What is
the probability that you achieve at least 7 tails?
•
(incorrect)
8. (2 points) It is known that a certain lacrosse goalie will
successfully make a save 89.55% of the time. Suppose that the

lacrosse goalie attempts to make 13 saves. What is the probabil-
ity that the lacrosse goalie will make at least 11 saves?
Let X be the random variable which denotes the number of
saves that are made by the lacrosse goalie. Find the expected
value and standard deviation of the random variable.
E(X) =
σ =
•
•
•
(incorrect)
9. (2 points) In a family with 3 children, excluding multiple
births, what is the probability of having exactly 2 girls?
Assume that having a boy is as likely as having a girl at each
birth.
•
(incorrect)
1
10. (2 points) A biotechnology company produced 192 doses
of somatropin, including 12 which were defective. Quality con-
trol test 11 samples at random, and rejects the batch if any of

the random samples are found defective. What is the probabil-
ity that the batch gets rejected?
•
(incorrect)
11. (2 points) A math professor finds that when he schedules
an office hour for student help, an average of 3.7 students
arrive.
Find the probability that in a randomly selected office hour, the
number of student arrivals is 2.
•
(incorrect)
12. (2 points) The mean number of patients admitted per day
to the emergency room of a small hospital is 3. If, on any given
day, there are only 6 beds available for new patients, what is
the probability that the hospital will not have enough beds to
accommodate its newly admitted patients?
answer:
•
(incorrect)
13. (2 points)
The number of accidents that occur at a busy intersection is

Poisson distributed with a mean of 3.5 per week. Find the prob-
ability of the following events.
A. No accidents occur in one week.
Probability =
B. 10 or more accidents occur in a week.
Probability =
C. One accident occurs today.
Probability =
•
•
•
(incorrect)
2
1. (2 points) An experiment consists of choosing a subset
from a fixed number of objects where the arrangement/order of
the chosen objects is not important. Determine the size of the
sample space when you choose the following:
(a) 2 objects from 24
Answer :
(b) 4 objects from 15
Answer :
(c) 7 objects from 25
Answer :

•
•
•
(incorrect)
2. (2 points) Determine the size of the sample space that
corresponds to the experiment of tossing a coin the following
number of times:
(a) 2 times
Answer:
(b) 3 times
Answer:
(c) n times
Answer:
•
•
•
(incorrect)
3. (2 points) Suppose you select a letter at random from the
word MISSISSIPPI.
The probability of selecting the letter I is
The probability of selecting the letter S is
The probability of selecting the letters P or M is
The probability of not selecting the letter M is

•
•
•
•
(incorrect)
4. (2 points) A fun size bag of M&Ms has about 18 candies.
You open one of the bags and discover:
3 Blues, 3 Yellows, 5 Browns, 4 Reds and 3 Greens.
The probability of choosing a brown is .
The odds in favor of choosing a yellow is
The probability of choosing either a blue or a red is
The odds against a green being chosen is
•
•
•
•
(incorrect)
5. (2 points) Look at these tiles.
Haley puts these 12 tiles in a bag and shakes. Then she pulls
out a tile at random.
What is the probability she picks a tile that is a multiple of 3?
• A. 412
• B. 812
• C. 84
• D. 48

•
(incorrect)
6. (2 points)
There are five Oklahoma State Officials: Governor (G), Lieu-
tenant Governer (L), Secretary of State (S), Attorney General
(A), and Treasurer (T). Take all possible samples without re-
placement of size 3 that can be obtained from the population of
five officials. (Note, there are 10 possible samples!)
(a) What is the probability that the governor is included in
the sample?
(b) What is the probability that the governor, attorney general
and the treasurer are included in the sample?
•
•
(incorrect)
7. (2 points) What is the probability that a family with three
children will have:
a) All boys?
b) One girl?
c) Two girls?
•

•
•
1
(incorrect)
8. (2 points) How many ways can a team of 25 hockey play-
ers choose a captain and two alternate captains?
•
(incorrect)
9. (2 points) A bookshelf has space for exactly 11 books. In
how many ways can the books be arranged on the bookshelf?
•
(incorrect)
10. (2 points) A park bench can seat 4 people. How many
seating arrangements are possible if 4 people out of a group of
12 want to sit on the park bench?
•
(incorrect)
11. (2 points) In how many ways can a person invite 4 out of
their 14 closest friends to a dinner party?

•
(incorrect)
12. (2 points) A company conducted a marketing survey
of college students and found that 213 own a bicycle and 112
owned a car. If 22 of those surveyed own both a car and a bicy-
cle, how many interviewed have a car or a bicycle?
•
(incorrect)
13. (2 points) A company conducted a marketing survey of
its clientele and found that 215 own an iPhone and 79 own an
iPad. If 27 clients own both an iPhone and an iPad, how many
interviewed have an iPhone or an iPad?
•
(incorrect)
14. (2 points) A standard Missouri state license plate consists
of a sequence of two letters, one digit, one letter, and one digit.
How many such license plates can be made?
A standard New York state license plate consists of a se-
quence of three letters followed by three digits. How many such
license plates can be made?

•
•
(incorrect)
15. (2 points) A test contains eight true/false questions. As-
suming you attempt each question, in how many different ways
could you answer the test?
•
(incorrect)
2

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