Question

In: Statistics and Probability

You would like to determine if teacher A gives different grades from teacher B in the...

You would like to determine if teacher A gives different grades from 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 whom passed the class. You also take a random sample of 70 students from teacher B, 56 of whom passed the class.

a) What is the estimate of the difference in proportion of students who pass? Find the estimate of pA − pB.

b) Is it appropriate to assume that the sampling distribution of the 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 are different. 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) State your conclusion for the hypothesis test, and then interpret the result in the context of the problem.

Expert Solution

Let denote the proportions of people who passed the class from teacher A and teacher B respectively.

a) The estimate of the difference in proportion of students who pass is

b) Since and , so it is appropriate to assume that the sampling distribution of the difference in proportions is normally distributed

c)

d) and e)

orchestra answered 2 years ago

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