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For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of 5260 permanent dwellings on an entire reservation showed that 1571 were traditional hogans. (b) Find a 99% confidence interval for . (Round your answers to three decimal places.) lower limit upper limit Give a brief interpretation of the confidence interval. 1% of all confidence intervals would include the true proportion of traditional hogans. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans. 1% of the confidence intervals created using this method would include the true proportion of traditional hogans. 99% of all confidence intervals would include the true proportion of traditional hogans. (c) Do you think that np>5 and nq>5 are satisfied for this problem? Explain why this would be an important consideration. Yes, the conditions are satisfied. This is important because it allows us to say that p^ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p^ is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p^ is approximately normal. Consider 202 binomial trials with 60 successes. (a) Is it appropriate to use a normal distribution to approximate the p^ distribution? (Select all that apply.) I No, it is not appropriate to use a normal distribution to approximate the distribution. Yes.np<5andnq<5Yes.np>5andnq>5Yes.np<5andnq<5Yes.np>5andnq<5 (b) Find a 95% confidence interval for the population proportion of successes p. (Round your answers to three decimal places.) lower limit upper limit (c) Explain the meaning of the confidence interval you computed. There is a 95% chance that the interval is one of the intervals containing the true proportion. There is a 5% chance that the interval is one of the intervals containing the true proportion. The probability that this interval contains the true proportion is 0.20 . The probability that this interval contains the true proportion is 0.80 . Consider 109 binomial trials with 36 successes. (a) Is it appropriate to use a normal distribution to approximate the p^ distribution? (Select all that apply.) Yes. n>5 and nq<5 Yes. n<5 and nq<5 No, it is not appropriate to use a normal distribution to approximate the distribution. Yes. np>5 and nq>5 Yes. n<5 and nq<5 (b) Find a 90% confidence interval for the population proportion of successes p. (Round your answers to three decimal places.) lower limit upper limit (c) Explain the meaning of the confidence interval you computed. There is a 20% chance that the interval is one of the intervals containing the true proportion. There is a 90% chance that the interval is one of the intervals containing the true proportion. Th.

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Please put answers below the boxes 1) A politician claims that he is supported by a clear majority of voters. In a recent survey, 35 out of 51 randomly selected voters indicated that they would vote for the politician. Use a 5% significance level for the test. Use Table 1. a. Select the null and the alternative hypotheses. H0: p = 0.50; HA: p ≠ 0.50 H0: p ≤ 0.50; HA: p > 0.50 H0: p ≥ 0.50; HA: p < 0.50 b. Calculate the sample proportion. (Round your answer to 3 decimal places.) Sample proportion c. Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.) Test statistic d. Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.) p-value e. What is the conclusion? Do not reject H0; the politician is not supported by a clear majority Do not reject H0; the politician is supported by a clear majority Reject H0; the politician is not supported by a clear majority Reject H0; the politician is supported by a clear majority 2) Consider the following contingency table. B Bc A 22 24 Ac 28 26 a. Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.) B Bc Total A Ac Total b. What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.) Probability c. What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.) Probability d. Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.) Probability e. Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.) Probability f. Are A and B mutually exclusive events? Yes because P(A | B) ≠ P(A). Yes because P(A ∩ B) ≠ 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0. g. Are A and B independent events? Yes because P(A | B) ≠ P(A). Yes because P(A ∩ B) ≠ 0. No because P(A | B) ≠ P(A). No because P(A ∩ B) ≠ 0. 3) A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2. a. Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.) Confidence interval to b. Construct a 99% confidence interval for the average number of customers who visit the .

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