Chapter 9.2, Problem 48E

To determine

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

Answer to Problem 48E

Sample proportion is lesser than 0.5

Explanation of Solution

Given:

  $\begin{array}{c}n=1000\\ x=482\end{array}$

Claim is Majority or equivalently more 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 statement is that the population proportion 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.

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

The sample proportion is

  $\widehat{p}=\frac{x}{n}=\frac{482}{1000}=0.485$

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