Question

A high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cookies. They collect a random sample of cookies, count the chips in each cookie, and calculate a 95% confidence interval for the average number of chips per cookie (18.6 to 21.3). Which interpretation of the 95% confidence interval is valid? Group of answer choices We are 95% certain that each cookie of this brand has approximately 18.6 to 21.3 chocolate chips. We expect 95% of the cookies to have between 18.6 and 21.3 chocolate chips. We would expect about 95% of all possible sample means from this population to be between 18.6 and 21.3 chocolate chips. We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie.

Answer 1

Answer:

Correct option:

We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie.

Step-by-step explanation:

The general formula for the (1 - α)% confidence interval for population mean is:

$CI=\bar x\pm CV \times SE_{\bar x}$

Here:

$\bar x$ = sample mean

CV = critical value

$SE_{\bar x}$ = standard error of mean.

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

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for the mean number of chocolate chips per cookie is (18.6, 21.3).

This 95% confidence interval implies that there is a 0.95 probability that the true mean number of chocolate chips per cookie is between 18.6 and 21.3.

Thus, the correct option is:

"We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie. "