Student researchers asked 84 students whether they were willing to take a survey. Some of the students were offered an incentive of a candy bar and some were not. The summary of the results are shown in the following table:

a. Find the proportion of those that received the incentive that took the survey and the proportion of those that did not receive the incentive that took the survey. 

b. Determine the Mean Group Diff statistic. 

c. When comparing two proportions, you could use the difference in the proportions or the Mean Group Diff as the statistic. How do these two statistics compare in this example? Will they always have the same relationship as in this example? Explain. 

d. Put the data from the table in the Multiple Proportions applet and make null distributions using both the difference in proportions and the Mean Group Diff statistic. Describe how these distributions are different. 

e. Based on your answer from part (c), explain why a distribution of Mean Group Diff statistics is skewed right when the distribution of differences in proportions is bell-shaped.  

Transcribed Image Text:

Agreed to take survey Refused to take survey Total Incentive No incentive 34 4 38 30 12 42 Total 64 16 80