Chapter 9, Problem R9.1RE

(a)

To determine

To Explain: the appropriate null and alternative hypotheses and the sample data give some evidence for ${\text{H}}_1$ .

Answer to Problem R9.1RE

  $H_0:\mu =64.2$

  $H_1:\mu \ne 64.2$

Explanation of Solution

Given:

Claim is mean differs from 64.2

Null hypothesis statement is that the population value should be equal to the value given in the claim.

  $H_0:\mu =64.2$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population mean should be 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.

  $H_1:\mu \ne 64.2$

Although the sample mean 63.5 differs from the hypothesized mean of 64.2 and the sample mean is giving the some evidence of $H_1$

(b)

To determine

To Explain: the appropriate null and alternative hypotheses and the sample data give some evidence for ${\text{H}}_1$ .

Answer to Problem R9.1RE

  $H_0:p=0.25$

  $H_1:p>0.25$

Although the sample proportion is 0.35 which is higher than 0.25, the sample proportion is giving the some evidence for $H_1$

Explanation of Solution

Given:

Claim is proportion is higher than 0.25

Null hypothesis statement is that the population value should be equal to the value given in the claim.

  $H_0:p=0.25$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion should be 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.

  $H_1:p>0.25$

Here p is the population proportion of students in that school who have been played in the rain.

  $\begin{array}{l}x=\text{ 28}\\ n\text{ = 80}\end{array}$

  $\begin{array}{c}\widehat{p}=\frac{x}{n}=\frac{28}{80}\\ =0.35\end{array}$

Although here the sample proportion is 0.35 which is higher than 0.25, the sample proportion is giving the some evidence for $H_1$