Confidence Intervals for Means

Complete each of the following calculations by providing thecorrect formula and values that you are using for eachproblem.

1) A sample size of n = 120 produced the sample mean of ? Ì… = 24.3.Assuming the population standard deviation ? = 5.2, compute a 99%confidence interval for the population mean. Interpret theconfidence interval.


2) Assuming the population standard deviation ? = 4, how largeshould a sample be to estimate a population mean with a margin oferror of 0.2 for a 95% confidence interval?


3) The manager of a plant would like to estimate the mean amount oftime a worker takes to complete a specific task. Assume thepopulation standard deviation for this task is 4.1 minutes.

a. After observing 70 workers completing the same type of task, themanager calculated the average time to be 12.7 minutes. Construct a90% confidence interval for the mean task time. Interpret theconfidence interval.

b. How large a sample size n should he observe to decrease themargin of error to 0.5 minutes for the 90% interval?

4) A sample of 25 was selected out of a specific population withmean equal to 18.4 and sample standard deviation of 3.6. Constructa 95% confidence interval for the mean of the population. Interpretthe confidence interval.


5) A group of students were randomly selected to participate in astudy that compared the female grades to the male grades for aspecific test. There were 15 females with a mean grade of 94.3 andsample standard deviation of 3.6. There were 12 males with a meangrade of 90.6 and sample standard deviation of 5.1. Construct a 90%confidence interval for the difference between the females’ andmales’ test grades. Interpret the confidence interval.