Question

A sample of 52 Elementary Statistics students includes 13 women. Assuming the sample is 4. random. . .

(a) Estimate the percentage of women taking Elementary Statistics with 98% confidence.

(b) At 10% significance, test whether less than 40% of the enrollment in all Elementary Statistics classes consists of women.

(c) If in fact 46% of the students in Elementary Statistics classes are women, find the power of the above test in detecting this parameter.

Answer 1

point estimate for thr proportion of women:

a)

for 98% confidence

b)c) This is a left tailed test

We will fail to reject the null (commit a Type II error) if we get a Z statistic greater than -1.2816. This -1.2816

Z-critical value corresponds to some p critical value ( p critical), such that

So I will incorrectly fail to reject the null as long as a draw a sample proportion that greater than 0.3129. To complete the problem what I now need to do is compute the probability of drawing a sample proportion greater than 0.3129 given p=0.46 . Thus, the probability of a Type II error is given by

power = 1-0.9833=0.0167