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, a typical response time is $200$milliseconds (about one-fifth of a second). Researchers collected data on response times of a random sample of$14$servers in Europe. A graph of the data reveals no strong skewness or outliers. The figure below displays Minitab output for a one-sample t interval for the population mean. Is there convincing evidence at the $5\%$significance level that the site’s claim is incorrect? Use the confidence interval to justify your answer.

Given in the question that, According to the site internettrafficreport.com, a typical response time is$200$milliseconds (about one-fifth of a second). Researchers collected data on response times of a random sample of $14$servers in Europe. A graph of the data reveals no strong skewness or outliers. The figure below displays Minitab output for a one-sample t interval for the population mean.

we need to find that the site’s claim is incorrect.

The output is

From the above yield, the $95\%$ confidence interval is $(158.22,189.64)$. It means that there are $95\%$chances that mean typical response time is somewhere in the range of $158.22$ and $189.64$ milliseconds. Here, $200$ doesn't lie in the processed confidence interval. Accordingly, there is sufficient proof to reason that case of site is wrong at $5\%$ significance level.