A researcher collected data from a random sample of 25 high school freshmen and found the mean of the sample to be 85.40 on the Test of Critical Thinking (TCT). She also calculated the standard deviation from the sample and discovered the value was 12.30. The average score on the Test of Critical Thinking for all high school seniors in a large school district is 90.00. The researcher wants to know if the mean TCT of the 25 high school freshmen in the random sample is different from the population’s (i.e., high school seniors) TCT mean.

a. Write out the null and alternative hypotheses associated with the research question.

b. What type of statistical test will you use to answer the proposed research question? (Note: Is this a z-test or a t-test?

c. What is the critical value at the 0.05 level of significance? Be sure and include whether this critical value is a z or t value and, if appropriate, include the degrees of freedom associated with this statistical test.

d. What is the observed value of the test statistic?