Question

One hundred volunteers were divided into two equal-sized groups. Each volunteer took a math test that involved transforming strings of eight digits into a new string that fit a set of given rules, as well as a third, hidden rule. Prior to taking the test, one group received 8 hours of sleep, while the other group stayed awake all night. The scientists monitored the volunteers to determine whether and when they figured out the rule. Of the volunteers who slept, 41 discovered the rule: of the volunteers who stayed awake, 13 discovered the rule. What can you infer about the proportions of volunteers in the two groups who discover the rule? Support your answer with a 95% confidence interval Let p1 be the proportion of volunteers who figured out the third rule in the group that slept and let P2 be the proportion of volunteers who figured out the third rule in the group that stayed awake all night The 95% confidence interval for (p1-p2) is CD (Round to the nearest thousandth as needed.) Interpret the result. Choose the correct answer below O There is insufficient evidence that the proportion of those who slept who figured out the rule is greater than the corresponding proportion of those who stayed awake. O There is sufficient evidence that the proportion of those who slept who figured out the rule is greater than the corresponding proportion of those who stayed awake.

Answer 1

Sample Samplumber of proportion Sample Size Sample ll 50| x1 = 41 -x =0.8200 Sample 21 n2= 501 x2 = 13 =0.2600 Level of significance a0.05 Critical value-た1.960 Margin of ETOPi(1-PP,(1-2 12 Lower Limit= (pi-p2)-(Margin of Error) = 0.398 pper Limt P-P2)+(Margin of Error)- 0.722 The 95% CI is (0.398, 0.722) or 0.398-p1-p2-0722. There is sufficient evidence that the proportion of those who slept who figured out the rule is greater than the corresponding proportion of those who stayed awake.