You would like to determine if teacher A gives different gradesfrom teacher B in the same class at a significance level of 0.01.You take a random sample of 85 students from teacher A, 61 of whompassed the class. You also take a random sample of 70 students fromteacher B, 56 of whom passed the class.
a) What is the estimate of the difference in proportion ofstudents who pass? Find the estimate of pA − pB.
b) Is it appropriate to assume that the sampling distribution ofthe difference in proportions is normally distributed?
c) Find a 90% confidence interval for the difference in part (a)and interpret it.
d) Your original goal is to test to see if the two teachers aredifferent. What are the hypotheses for this test?
e) Calculate the z-test statistic for the tests defined in part(d). f) Find the P-value for the test defined in part (d). g) Stateyour conclusion for the hypothesis test, and then interpret theresult in the context of the problem.
