Reference no: EM132853157

A Statistics professor has observed that for several years about 13% of the students who initially enroll in his Introductory Statistics course withdraw before the end of the semester. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will cut the dropout rate. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the dropout rate goes down significantly. The professor will have to pay for the software only if chooses to continue using it. He decides to use one of his classes this semester as a test case (his sample)

a) Define the parameter of interest and write the null and alternative hypotheses the professor will use.

b) Describe a Type I error in this context, and what the consequences would be (who would be harmed by this type of error?).

c) Describe a Type II error in this context, and what the consequences would be (who would be harmed by this type of error?).

d) Based on your answers to (b) and (c), what level of α would you use for this test? Explain your choice.

e) Discuss the professor's method of choosing a sample. How might this impact his ability to generalize his results to all of his students?

f) Suppose that the professor used his trial run to calculate a 98% confidence interval for the true dropout rate using the software. His interval was (0.092, 0.120). Can he conclude that the dropout rate was lower with the software? Explain.

g) What if the interval in (f) had been (0.103, 0.137). Could he conclude that the dropout rate was lower with the software? Explain.