Question

When testing a claim that the majority of adult Americans are against the death penalty for a person convicted of murder, a random sample of 491 adults is obtained, and 27% of them are against the death penalty (based on data from a Gallup poll). Find the P-value. Round to 4 decimals when necessary.

Answer 1

Using the z-distribution, it is found that the p-value is of 1.

At the null hypothesis, it is tested that the majority is not against the death penalty, that is:

$H_0: p \neq 0.5$

At the alternative hypothesis, it is tested that the majority is against the death penalty, that is:

$H_1: p > 0.5$

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

• $\overline{p}$ is the sample proportion.

• p is the proportion tested at the null hypothesis.

• n is the sample size.

In this problem, the parameters are: $\overline{p} = 0.27, p = 0.5, n = 491$.

Then, the value of the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.27 - 0.5}{\sqrt{\frac{0.5(0.5)}{491}}}$

$z = -10.19$

Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is greater than a value, the p-value is of 1.

A similar problem is given at brainly.com/question/16313918