stats word problem

Question

A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 124 students who averaged 36.8 minutes concentrating on their professor during the hour lecture. The standard deviation was 13.1 minutes. Round answers to 3 decimal places where possible.

a. With 95% confidence the population mean minutes of concentration is between ____ and ____ minutes. 

b. If many groups of 124 randomly selected members are studied, then a different confidence interval would be produced from each group. About _____ percent of these confidence intervals will contain the true population mean minutes of concentration and about  ______percent will not contain the true population mean minutes of concentration. 

Answer 1

Hi Jessica! Here's how I approached this question:

First, we need to figure out whether to use a z-interval or t-interval. Because the question asks for the interval of the mean minutes of concentration, we need to use a one-sample t-interval (because a z-interval is for proportions).

We can find the exact interval using a calculator and entering the mean, standard deviation, sample size, and confidence level. I found the confidence interval to be (34.471, 39.129).

This means that with 95% confidence, the population mean minutes of concentration is between 34.471 and 39.129 minutes. 

Because the confidence level used is 95%, if many groups of 124 randomly selected members are studied, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean minutes of concentration and about 5 percent will not contain the true population mean minutes of concentration.