Question

For each of the single sample t-tests below (problem 1-3), please include:
1) The null and alternative hypotheses (can be written in notation or as a sentence)
2) Calculate (show all work):
a) The estimated population variance
b) The variance of the distribution of means
c) The standard deviation of the distribution of means
3) Degrees of freedom
4) The cutoff sample score on the comparison distribution at which the null hypothesis
should be rejected (cutoff scores)
5) The sample’s score on the comparison distribution (e.g. t-obtained) (show all work)
6) Decide whether to reject the null hypothesis
7) State your conclusion in APA format (make sure to report what groups you are comparing
(and their means), what the DV is, whether it was significant or not and your test statistic (t)
(see the lecture slides for examples).
Problem 1) An investigator thinks that people under the age of forty have vocabularies that
are different than those of people over sixty years of age. The investigator administers a
vocabulary test to a group of 31 younger subjects. Higher scores reflect better performance.
The mean score for younger subjects was 14.0 and the standard deviation of younger
subject's scores was 5.0. The mean score for older subjects (the known population) was 20.0.
Does this experiment provide evidence for the investigator's theory? Please test the
investigator's theory using an alpha level of .05.

Answer 1