Unit 5-Sampling Distributions HW 3-Sampling Distribution of a Difference in Sample Proportions Name: Period: Suppose that there are two large high schools, each with more than 2000 students, in a certain town. At School 1, 70% of students did their homework last night. Only 50% of the students at School 2 did their homework last night. The counselor at School 1 takes an SRS of 100 students and records the proportion that did homework. School 2's counselor takes an SRS of 200 students and records the proportion that did homework. School 1's counselor and School 2's counselor meet to discuss the results of their homework surveys. After the meeting, they both report to their principals that 1-2 = 0.10. (a) Describe the shape, center, and spread of the sampling distribution of p1 - 2 (b) Find the probability of getting a difference of 0.10 or less between the two surveys. (c) Does the result in part (b) give us reason to doubt the counselor's reported value?