Chapter 9.3, Problem 81E

(a)

To determine

To Explain: the state an appropriate pair of hypothesis for a significance test in this setting.

Answer to Problem 81E

  $H_0:\mu =200$

  $H_1:\mu \ne 200$

Explanation of Solution

Given:

Claim is that the mean is 200 milliseconds

The null hypothesis statement is that the population value is equal to the value given in the claim:

  $H_0:\mu =200$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

  $H_1:\mu \ne 200$

  $\mu$ is the mean response time of servers in Europe

(b)

To determine

To Explain: the condition for performing the test in part (a).

Answer to Problem 81E

All conditions are satisfied

Explanation of Solution

The three conditions for are: Random, independent, Normal/ Large sample.

Random: Satisfied, because the sample is a random sample.

Independent: satisfied, because the sample of 14 server is less than 10% of the population of all servers

Normal/Large sample: Satisfied, because a graph of the data reveals neither strong skewness nor outliers.

Since all conditions are satisfied, it is suitable to perform a hypothesis test for the population mean $\mu$ .

(c)

To determine

To Explain: the conclusion would make for a test of the hypothesis in part (a) at the 5% significance level.

Answer to Problem 81E

There is enough convincing proof that the mean response time for serves in Europe is different from 200 milliseconds.

Explanation of Solution

Given:

95% confidence interval:

(158.22, 189.64)

A 95% confidence interval corresponds with a hypothesis test with significance level 100%-95%=5%.

It is observed that the confidence interval is not having 200, which means that it is unlikely that the mean response time for severs in Europe is 200 milliseconds and therefore there is enough convincing proof that the mean response time for serves in Europe is different from 200 milliseconds.

(d)

To determine

To Explain: the convincing evidence that the mean response time of servers in the United States is different from 200 milliseconds, justify the answer.

Answer to Problem 81E

No

Explanation of Solution

These data is about servers in Europe and therefore would not be able to make a final conclusion for the servers in the United States, as the servers could have different response time from the server in Europe. This means that there is no convincing proof that the mean response time of servers in the United States is different from 200 milliseconds.