A study of teenagers found the following information on length of time (in minutes) each talked on phone. Find the 95% confidence interval of the true differences in means.

Solution: We are now testing the hypotheses:

We will use a two-tailed t-test to test the null hypothesis. Again, with the aid of Statdisk, we compute the value of the t-statistics (since the sample size is big enough we are going to use a normal approximation):

The value of the test statistics is equal to 5.3430, and the critical values are. This means that we reject the null hypothesis. Now, the 95% confidence interval is given by