How long does it take for a chunk of information to travel from one server to another and back on the Internet? According to the site internettrafficreport.com, the average response time is 200 milliseconds (about one-fifth of a second). Researchers wonder if this claim is true, so they collect data on response times (in milliseconds) for a random sample of 14 servers in Europe. A graph of the data reveals no strong skewness or outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The 95% confidence interval for the mean response time is 158.22 to 189.64 milliseconds. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 5% significance level?

d. Do we have convincing evidence that the mean response time of servers in the United States is different from 200 milliseconds? Justify your answer.