Question

true or falseSuppose a 95% confidence interval for the population proportion of students at your school who reg-ularly drink alcohol is (0.61,0.67). The inference is that you can be 95% confident that the sampleproportion falls between 0.61 and 0.67.

Answer 1

Answer:

The provided statement is False.

Step-by-step explanation:

A (1 - α)% confidence interval for population proportion is given by:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}$

The 95% confidence interval for the population proportion of students at your school who regularly drink alcohol is,

CI = (0.61, 0.67)

A (1 - α)% confidence interval for a population parameter implies that there is (1 - α) probability that the true parameter value is contained in the interval.

Or, there is (1 - α)% confidence that the confidence interval consists of the true population parameter value.

The 95% confidence interval for the population proportion of students who  who regularly drink alcohol indicates that there is 0.95 probability that the true proportion values is included in the interval (0.61, 0.67).

Or, we are 95% confident that the 95% confidence interval, i.e. (0.61, 0.67) includes the true proportion of students who  who regularly drink alcohol.

Thus, the provided statement is False.