Questions: Suppose the null hypothesis is not rejected. What would be an appropriate conclusion in the context of the problem? We do not have enough evidence to conclude that the percentage of males who are college graduates is still the same. We have enough evidence to conclude that the percentage of males who are college graduates has gone down. We do not have enough evidence to conclude that the percentage of males who are college graduates has gone down. We have enough evidence to conclude that the percentage of males who are college graduates has gone up. We have enough evidence to conclude that the percentage of males who are college

Suppose the null hypothesis is not rejected. What would be an appropriate conclusion in the context of the problem?

We do not have enough evidence to conclude that the percentage of males who are college graduates is still the same.

We have enough evidence to conclude that the percentage of males who are college graduates has gone down.

We do not have enough evidence to conclude that the percentage of males who are college graduates has gone down.

We have enough evidence to conclude that the percentage of males who are college graduates has gone up.

We have enough evidence to conclude that the percentage of males who are college

Transcript text: Suppose the null hypothesis is not rejected. What would be an appropriate conclusion in the context of the problem? We do not have enough evidence to conclude that the percentage of males who are college graduates is still the same. We have enough evidence to conclude that the percentage of males who are college graduates has gone down. We do not have enough evidence to conclude that the percentage of males who are college graduates has gone down. We have enough evidence to conclude that the percentage of males who are college graduates has gone up. We have enough evidence to conclude that the percentage of males who are college

Solution

Solution Steps

Step 1: Hypothesis Setup

We are testing the null hypothesis \( H_0: p = p_0 \) against the alternative hypothesis \( H_a: p \neq p_0 \), where:

\( p_0 = 0.5 \) (the hypothesized population proportion of males who are college graduates)
\( \hat{p} = 0.48 \) (the sample proportion of males who are college graduates)
\( n = 100 \) (the sample size)

Step 2: Test Statistic Calculation

The test statistic \( Z \) is calculated using the formula: \[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] Substituting the values: \[ Z = \frac{0.48 - 0.5}{\sqrt{\frac{0.5(1 - 0.5)}{100}}} = \frac{-0.02}{\sqrt{\frac{0.25}{100}}} = \frac{-0.02}{0.05} = -0.4 \]

Step 3: P-value Calculation

The p-value associated with the test statistic \( Z = -0.4 \) is calculated to be: \[ \text{P-value} = 0.6892 \]

Step 4: Critical Region

For a two-tailed test at a significance level \( \alpha = 0.05 \), the critical region is defined as: \[ Z < -1.96 \quad \text{or} \quad Z > 1.96 \]

Step 5: Conclusion

Since the calculated p-value \( 0.6892 \) is greater than the significance level \( \alpha = 0.05 \), we do not reject the null hypothesis. Therefore, we conclude: \[ \text{Conclusion: We do not have enough evidence to conclude that the percentage of males who are college graduates has changed.} \]