Question

Suppose a national survey conducted among a simple random sample of 1522 American adults, 806 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

Answer:

Null Hypothesis, $H_0$ : p $\leq$ 0.50

Alternate Hypothesis, $H_a$ : p > 0.50

Step-by-step explanation:

We are given that a national survey conducted among a simple random sample of 1522 American adults, 806 indicate that they think the Civil War is still relevant to American politics and political life.

We have to test the hypothesis to determine if the majority (more than 50%) of Americans think the Civil War is still relevant.

Let Null Hypothesis, $H_0$ : p $\leq$ 0.50  {means that less than or equal to 50 percent of Americans think the Civil War is still relevant}

Alternate Hypothesis, $H_a$ : p > 0.50  {means that more than 50 percent of Americans think the Civil War is still relevant}

The test statistics that will be used here is One-sample proportion test;

               T.S. = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = % of American adults who think that the Civil War is still relevant  in a sample of 1522 adults = $\frac{806}{1522}$

           p = population proportion

            n = sample of american adults surveyed = 1522

So, this is the correct hypotheses for conducting a hypothesis test.