Chapter 9.3, Problem 82E

(a)

To determine

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

Answer to Problem 82E

  $H_0:\mu =40$

  $H_{1`}:\mu \ne 40$

Explanation of Solution

Given:

Claim is that the mean is 40 ounces

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

  $H_0:\mu =40$

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.

  $H_{1`}:\mu \ne 40$

  $\mu$ is the mean daily water intake of U.S. adults.

(b)

To determine

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

Answer to Problem 82E

All conditions are satisfied.

Explanation of Solution

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

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

Independent: satisfied, because the sample of 24 U.S. adults is less than 10% the population of all U.S. adults

Normal/Large sample: Satisfied, because a graph of the data shows no outliers and no skewed

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

(c)

To determine

To Explain: the conclusion would make for a test of the hypothesis in part (a) at the 10% significance level.

Answer to Problem 82E

There is convincing proof that the mean daily water intake is different from 40 ounces.

Explanation of Solution

Given:

90% confidence interval:

(30.35, 36.92)

A 90% confidence interval associates with a hypothesis test with significance level 100%-90%=10%.

It is observed that the confidence interval is not having 40, which means that it is unlikely that the mean daily water intake is 40 ounces and therefore there is convincing proof that the mean daily water intake is different from 40 ounces.

(d)

To determine

To Explain: the convincing evidence that the amount of water U. S. Children drink per day differs from 40 ounces, justify the answer.

Answer to Problem 82E

No

Explanation of Solution

The data is based on data for U.S. adults and therefore it will not be able to make a conclusion for the U.S. children could have different daily water intakes from the adults.

It means that we do not have enough convincing evidence that the mean daily water intake of U.S. children is different from 40 ounces.