When you hand in your test, do you think you will get a higher score than you actually do? A professor collected data to answer this question in a college mathematics course. After finishing a test, the 27 students in the class wrote their predicted scores on their tests, and these were compared with the actual scores after they were graded. The mean predicted score was 83.7 (SD = 12.8), the mean actual score was 81.2 (SD = 15.6), and the mean of the differences was 2.5 (SD = 8.6). Null: The average difference in test scores (predicted – actual) is 0 (μ_d = 0). Alternative: The average difference in test scores (predicted – actual) is greater than 0 (μ_d > 0). 

a. What is the observed statistic for this study? 

b. Assuming a true null hypothesis, we simulated this study and found 5,000 mean differences that are shown in the null distribution below. Based on where the observed statistic lies in the null distribution, does the p-value appear to be very small? 

c. How many standard deviations is the observed mean difference above the mean of the null distribution? (i.e., What is the standardized statistic?) 

d. Based on your standardized statistic, is there strong evidence that college students in this type of mathematics class predict test scores that are higher than their actual scores on average? Explain. (Assume we have a representative sample of all students taking this mathematics class at this college.)

Transcribed Image Text:

Mean = 0.000 SD = 1.694 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Average difference