91Ó°ÊÓ

The claim is mean differs from $64.2$

The null hypothesis asserts that the population value should be the same as the claim value.

$H_0:\mathrm{μ}=64.2$

Either the null hypothesis or the alternative hypothesis is the assertion. The null hypothesis asserts that the population means should be the same as the claim value. If the claim is the null hypothesis, the alternative hypothesis statement is the polar opposite of the claim.

$H_1:\mathrm{μ}≠64.2$

Although the sample mean of $63.5$differs from the hypothesized mean of $64.2$ there is some indication of $H_1$ in the sample averages.

The null hypothesis asserts that the population value should be the same as the claim value.

$H_0:p=0.25$

Either the null hypothesis or the alternative hypothesis is the assertion. The null hypothesis asserts that the population proportion should be the same as the claim value. If the claim is the null hypothesis, the alternative hypothesis statement is the polar opposite of the claim.

$H_1:p>0.25$

Here, $p$ is the percentage of pupils in that school who have played in the rain.

$$\begin{gathered} x=28 \\ n=80 \\ \hat{p}=\frac{x}{n}=\frac{28}{80} \\ =0.35 \end{gathered}$$

Despite the fact that the sample proportion is $0.35$which is greater than $0.25$the sample proportion supports $H_1$