Question

1. According to a study, 21% of 507 female college students were on a diet at the time of the study.

a) Construct a 99% confidence interval for the true proportion of all female students who were on a diet at the time of this study.

b) Explain what this interval means.

c) Is it reasonable to think that only 17% of college women are on a diet?

Answer 1

a)

We know that 99% CI for true proportion is given by:

b)

We can say with 99% confidence that the true proportion lies in the above interval.

c)

Since the obtained 99% confidence interval contains 0.17, so at 1% level of significance, we can say that it is reasonable to think that only 17% of college women are on a diet.