One-Sample t-Tests
A Story Problem
An educational consulting firm claims its new
reading curriculum improves the mean reading
score of children.
Last year the mean score in the school system (for
all the students) was 100.
For each of the following scenarios, do the data
support the claim that the new curriculum
improves the mean score?
Scenario 1
A random sample of 100 students was taught the
new curriculum.
Their mean score was 102 with an SD of 10.
 Did this show significant improvement or just
random fluctuation — sampling error?
Scenario 2
A random sample of 36 students was taught the
new curriculum.
Their mean score was 102 with an SD of 10.
 Did this show significant improvement or just
random fluctuation — sampling error?
Scenario 3
A random sample of 400 students was taught the
new curriculum.
Their mean score was 102 with an SD of 5.
 Did this show significant improvement or just
random fluctuation — sampling error?
Scenario 4
A random sample of 100 students was taught the
new curriculum.
Their mean score was 101 with an SD of 16.
 Did this show significant improvement or just
random fluctuation — sampling error?
Scenario 5
A random sample of 400 students was taught the
new curriculum.
Their mean score was 99 with an SD of 4.
 What is your conclusion? (Hint: Should we use a
one-tailed or two-tailed t-test?)
The Null Hypothesis
 What was the null hypothesis for the story
problem (in words, general idea)?
 What was the formula that states the null
hypothesis?
 How do we use the null hypothesis to set up the
formula for the test statistic (in this case, a ttest)?
Key Terms for Hypothesis Testing
 Null hypothesis
 Test statistic: How discrepant is the computed
value (based on the sample) from the value
expected if the null hypothesis is true?
 Standard error
 Critical value
More Key Terms
 Comparing the test-statistic value to the critical
value — is it discrepant enough?
 Reject or fail to reject the null hypothesis.
 P-value — probability of Type I error.
 P-value must be small — the smaller the better
(the higher the level of significance); less than
.05 (that’s 5/100).
What a t-Test Can’t Tell Us
 Whether the consultant is honest or not.
 Whether the random sample (or other type of
probability sample) was drawn correctly.
 The cost (e.g., money or effort) of changing
curricula — even if the new curriculum is
significantly better, statistically, is it worth
making the change?