Question

Assuming assumptions have been met (e.g., sample sizes, similar variances), for each of the following scenarios, determine whether a single mean z test, single mean t test, paired means t test, independent means t test, one-way between groups ANOVA, or one-way within groups ANOVA should be used. Explain why that procedure is appropriate.

A. Are the mean sale prices of two-bedroom homes different in Oregon, Washington, and Idaho? Data are collected from random samples of two-bedroom homes from each state. [5 points]

One way between groups ANOVA because you’re looking at 3+ independent groups and data is collected

B. Are scores on a new quantitative measure of statistics anxiety different for students taking PSY 298 online compared to students taking PSY 298 on campus? [5 points]

C. SAT-Math scores are normally distributed with a mean of 500 and standard deviation of 100. Is the average SAT-Math score of all psychology majors at one large university different from the national norm of 500 [5 points] Single sample z-test because we’re comparing the mean sat math score in a population to the mean of the sat score at a university.

D. Do students score differently on a measure of statistics knowledge at the beginning of PSY 298, end of PSY 298, and one year after completing PSY 298? Data are collected from a sample of 50 students. Each student takes the same quantitative measure of statistics knowledge at the beginning of PSY 298, end of PSY 298, and one year after completing PSY 298. [5 points]

Answer 1

Assuming the assumptions are met,

A. For a scenario of testing the possible difference of mean sale prices of two-bedroom homes in Oregon, Washington, and Idaho, one should use One-way between groups ANOVA since there are more than 2 groups to be compared.

B. To test for difference in a new quantitative measure of statistics anxiety for students taking PSY 298 online and students taking PSY 298 on campus, a two-sample t-test or a two-sample Z-test can be used since the problem at hand is a comaprison between two groups. Based on the sample size the slecetion of the procedure can be more precise. If the sample size is large, Z-test is preferred otherwise t-test yields better results.

C. In comparing normally distributed SAT-Math scores of all the psychology majors at one large university with that of national norms, a one-sample Z-test or a one-sample t-test is preferred since a computed average score of  psychology majors at one large university is being compared with a hypothesized (specified) value of national level. The choice between a Z-test or a t-test is based on the sample size. If the size of the sample is large, Z-test prefrred to a t-test.

D. For comparing the performance of students in a measure of statistics knowledge at the beginning of PSY-298, at the end of PSY-298 and after one year of completion of PSY-298, one should use One-way within gruoups ANOVA. The one-way within group ANOVA is also called as ANOVA with repeated measures. This procedure is used when a single group of subjects are subjected to more than two treatments/trials.