2. Quick review
• The information needed to compare groups is usually all
given to us (means, standard deviations, variances)
• Z-tests – ______________ means (rather than
_______________scores); compare sample to
______________________________
o Why did we use the distribution of means?
• __________________________________________________
o The ______________ is a good tool to use to estimate the population
(which is harder to estimate)
4. t-tests
• t-test – hypothesis testing where the population
________________________ is unknown
• i.e. – you want to compare
________________________, but you don’t know if the
__________________________ between them
___________________ anything without the variance!
• 2 types
o t-test for single sample
o t-test for dependent means
5. t-test for single sample
• One sample vs population
• How do you estimate the population variance?
o Rule: The __________________ of a _________________________(random group
of people) tends to be slightly ________________________________than the
variance of the population (___________________________) –
found through research
Old formula
SD2 = Σ(X-M)2
N
o We need an __________________________to make our results
more accurate – slightly change the variance formula
New formula
S2 = Σ(X-M)2
N-1
6. S2 = Σ(X-M)2
N-1
• Dividing by a slightly smaller number (N-1) makes
the result __________________________, correcting for
the tendency to ______________________________ pop
variance
• ________________________________________= N – 1 –
keeping 1 individual ____________________while the
others are allowed to ______________________
• New, simpler terms:
Σ(X-M)2 = _______________________
N–1 = ________
7.
8. t score
• SO we have the new pop variance, the new
DofM, and now we can calculate a new type of
score
t = M-u M = ___________________
Sm u = __________________
Sm = ________________
9. t distribution
• Now that we have (more accurately) a new type of
score, we need to use a new distribution
• t-distributions depend on the ______you have (and
therefore ________________________)
• Higher df (higher sample size) =
_____________________ to normal curve
• T-table is in your book, ____________________________
10. t-test single sample Example
• Hypothesis: Statistics students who had calculus in
high school will have ________________ GPAs then
statistics students in general.
• 1. Begin with stating what your two populations are:
o ________________________________– Students who had calculus GPAs
o ____________________________________– All stats students’ GPAs
• 2. Next, state your hypotheses:
o ________________________________________– there is ___________difference
between students who had calculus and all stats students.
o __________________________________________– there ______a
difference between students who had calculus and all stats
students.
• 3. Goal:
o What is the probability of getting certain results, if there is no difference
11. • 4. Determine probability:
o .01 (1%)
• 5. Determine your sample’s t-score (if sample mean
is ___, pop mean is ____ and DofM SD is ___)
t = M-u / Sm =6 – 3/1 = 3/1 =3
• 6. Decide whether to reject or accept the null
hypothesis with a sample size of 30
12. t-table
df = ___
probability = ____
One or two tailed = _____
t-score = _____
Cut-off value = _________
__________________
