Chapter 9.2, Problem 47E

To determine

To Explain: that it isn’t necessary to carry out a significance test in this setting.

Answer to Problem 47E

Sample proportion is bigger than 0.5

Explanation of Solution

Given:

  $\begin{array}{c}n=1060\\ x=551\end{array}$

Claim is less than half of the parents or equivalently less than 50%

Formula used:

Sample proportion is

  $\widehat{p}=\frac{x}{n}$

Calculation:

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

  $\begin{array}{c}{H}_0:p=50\%=0.5\\ H_1:p<0.5\end{array}$

The sample proportion is

  $\widehat{p}=\frac{x}{n}=\frac{551}{1060}=0.5198$

There is testing the claim if the population proportion is less than 0.5. Although, the sample proportion is bigger than 0.5 and therefore the sample proportion does not give any proof that the alternative hypothesis could be true.