The exercises in Chapter 7 included a study designed to measure the number of chocolate chips in a bag of Chips Ahoy cookies (Warner \& Rutledge, 1999). From this example, for the sample of 18 bags of cookies, the mean \((\bar{X})\) and standard deviation (s) of the number of chips were found to be \(1,261.00\) and 114.01 , respectively. Imagine you want to estimate the average number of chocolate chips in the population of Chips Ahoy bags of cookies. Calculate a \(95 \%\) confidence interval for the mean for this set of data.

a. State the desired level of confidence.

b. Calculate the confidence interval and confidence limits.

(1) Calculate the standard error of the mean \(\left(s_{\bar{X}}\right)\).

(2) Calculate the degrees of freedom (df) and identify the critical value of \(t\).

(3) Calculate the confidence interval and confidence limits.

c. Draw a conclusion about the confidence interval.