Question

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of $1000$registered voters, $482$favor the proposition. Explain why it isn’t necessary to carry out a significance test in this setting.

Short answer

Sample proportion is less than$0.5$

Step-by-step solution

Given Information

It is given that $n=1000$

$x=482$

Claim is greater than$50\%$

Explanation and Calculation

As per given data:

Null Hypothesis: $H_0:p=50\%=0.5$

Alternative Hypothesis: $H_1:p>0.5$

Sample proportion is calculated as:

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

Claim is population proportion less than $0.5$. Sample proportion after calculation is less than $0.5$.

So, there is no proof given by sample proportion that alternative hypothesis could be true.