Chapter 9, Problem T9.12SPT

(a)

To determine

To Explain: the state appropriate hypothesis for testing the manager’s belief.

Answer to Problem T9.12SPT

  $H_0:\mu =41.6$

  $H_1:\mu <41.6$

Explanation of Solution

Given:

Claim is that mean is less than 41.6 (younger)

Explanation:

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

  $H_0:\mu =41.6$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

  $H_1:\mu <41.6$

  $\mu$ is the mean age of the employees at the company.

(b)

To determine

To Explain: the condition for performing a test of the hypothesis in part (a) and find whether each condition is met.

Answer to Problem T9.12SPT

All conditions are satisfied.

Explanation of Solution

The three conditions are: Random, independent (10% condition), Normal/Large sample.

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

Independent: Satisfied, because the sample of 12 employees is less than 10% of the population of all employees of 12 employees is less than 10% of the population of all employees

Normal/ Large sample: Satisfied, because the pattern in the normal quintile plot is roughly

Linear, which indicates that the distribution is approximately Normal

Since all conditions are satisfied, it is appropriate to perform a hypothesis test for the population mean

(c)

To determine

To Explain: that the P-value of the test is 0.003, interpret this value and conclusion would make.

Answer to Problem T9.12SPT

There is a 0.3% probability of getting the sample results or more extreme, when the mean age of the company’s employees is 41.9 years.

Explanation of Solution

Given:

  $P=0.003=0.3\%$

Claim: mean less than 41.9.

The claim is either the null hypothesis or the alternative hypothesis. The null hypotheses 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 null hypothesis.

  $\begin{array}{c}{H}_0:\mu =41.9\\ H_1:\mu <41.9\end{array}$

The P-value is the probability of getting the value of the test statistic or a value more extreme, once the null hypothesis is true.

There is a 0.3% probability of getting the sample results or more extreme, when the mean age of the company’s employees is 41.9 years.