Chapter 9.3, Problem 67E

(a)

To determine

To Explain: the state appropriate hypothesis for the quality-control department to test.

Answer to Problem 67E

  $H_0:\mu =10.5$

  $H_1:\mu <10.5$

Explanation of Solution

Given:

Claim is that mean is less than 10.5

The null hypothesis states that the population value is equal to the value mentioned in the claim:

  $H_0:\mu =10.5$

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.

  $H_1:\mu <10.5$

13y $\mu$ is the mean battery lifetime.

(b)

To determine

To find: the conditions for performing the test in part (a) are met.

Answer to Problem 67E

Large sample condition is not satisfied.

Explanation of Solution

Given:

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

Random: Satisfied, because the tablets were randomly selected.

Independent: Satisfied, because sample of 20 tables is than 10% of the population of all tablets

Normal/ Large sample: Not satisfied, because the sample of 20 tablets is small and the distribution in the dot plot is strongly skewed.

Since the Normal/Large sample condition is not satisfied it is not appropriate to perform a hypothesis test for the population mean.