Question

(5 points) The Civil War. Suppose a national survey conducted among a simple random sample of 1529 American adults, 811 indicate that they think the Civil War is still relevant to American politics and political life. NOTE: While performing the calculations, do not used rounded values. For instance, when calculating a p-value from a test statistic, do not use a rounded value of the test statistic to calculate the p-value. Preserve all the decimal places at each step. Enter at least 4 decimal places for each answer in WeBWorK. 1. What are the correct hypotheses for conducting a hypothesis test to determine if the majority (more than 50%) of Americans think the Civil War is still relevant.

Answer 1

`H_0: \pi\leq0.5\\\\H_a: \pi>0.5`

It can be claimed that there is evidence that the majority of Americans think the Civil War is still relevant.

Explanation:

To test the claim that the majority of Americans think the Civil War is still relevant, the hypothesis should be:

`H_0: \pi\leq0.5\\\\H_a: \pi>0.5`

We assume a level of significance of 0.05.

The proportion for this sample is p=811/1529=0.53.

The standard deviation is:

`\sigma_p=\sqrt(\pi(1-\pi))/(N) }= \sqrt(0.5*0.5)/(1529) }=0.0128`

The z-value for this is:

`z=(p-\pi-0.5/N)/(\sigma)=(0.53-0.5-0.5/1529)/(0.0128)=(0.0297)/(0.0128)=2.3206`

The p-value for this one-tailed test is then P=0.01015.

The p-value is smaller than the significance level, so the null hypothesis is rejected.

It can be claimed that there is evidence that the majority of Americans think the Civil War is still relevant.