A health researcher wanted to know if there was a difference in success rates between three methods of quitting smoking: A, B, and C. She designed a study with 15 participants, 5 in each group, and asked participants to track how many cigarettes they smoked in a 2-week period. In the results of her study, she reported as follows: “The means of the groups (Method A: M = 156, SD = 33.6; Method B: M = 163, SD = 34.4; Method C: M = 145, SD = 48.4) did not differ significantly, F(2, 12) = .27; ns.”

1)Provide an example of a study that would utilize a t test for a single sample. List three differences in how you would carry out hypothesis testing for a t test for a single sample versus for a F test

An example of a study that would utilize a t test for a single sample could be a research investigation on the effectiveness of a new teaching method in improving students' test scores. In this study, the researcher could randomly select a sample of students from a specific grade level, administer a standardized test to them, introduce the new teaching method, and then administer the same standardized test again after the implementation of the teaching method. The researcher would collect the pre- and post-test scores of the students.

Three differences in how hypothesis testing would be carried out for a t test for a single sample compared to an F test are:

1) Step 1: Null and Alternative Hypotheses: In a t test for a single sample, the null hypothesis typically states that there is no significant difference between the mean of the sample and the population mean. The alternative hypothesis would state that there is a significant difference. In contrast, for an F test, the null hypothesis states that there is no difference between the variances of two or more populations, while the alternative hypothesis states that there is a significant difference in variances.

2) Step 2: Test Statistic: For a t test, the test statistic used is the t-value, which is calculated by dividing the difference between the sample mean and the population mean by the standard error of the mean. This t-value is then compared to the critical value from the t-distribution to determine statistical significance. In an F test, the test statistic is the F-value, which is the ratio of the variances of the groups being compared. The F-value is compared to the critical value from the F-distribution to determine statistical significance.

3) Step 3: Interpretation: When conducting a t test for a single sample, the researcher looks for evidence to either reject or fail to reject the null hypothesis. If the t-value calculated exceeds the critical value, then the researcher may reject the null hypothesis and conclude that there is a significant difference between the sample mean and the population mean. In the case of an F test, the researcher looks for evidence to either reject or fail to reject the null hypothesis. If the calculated F-value exceeds the critical value, the researcher may reject the null hypothesis and conclude that there is a significant difference in variances.