Question

The mayor of a town read an article that claimed the national unemployment rate was 8%. They suspected that the unemployment rate was lower in their town, so they took a sample of 128 residents to test H:p= 0.08 versus Ha:p < 0.08, where p is the proportion of residents that are unemployed. They found that 8 residents in the sample were unemployed. Using these results, they calculated a test statistic of z Ž -0.73 and a P-value of approximately 0.23.

Answer 1

The final answer is that the town should not reject the null hypothesis (H0: p = 0.08) as the p-value of approximately 0.23 is greater than the significance level of 0.05.

Step-by-step explanation:

The mayor conducted a hypothesis test to determine if the unemployment rate in their town is lower than the national average of 8%. The null hypothesis (H0) states that the town's unemployment rate is equal to the national average (p = 0.08), while the alternative hypothesis (Ha) suggests it is lower (p < 0.08). The test statistic, z = -0.73, indicates how many standard deviations the sample proportion is from the hypothesized population proportion.

The p-value, approximately 0.23, is the probability of observing a test statistic as extreme as -0.73 or more extreme, assuming the null hypothesis is true. Since the p-value is greater than the commonly used significance level of 0.05, there is not enough evidence to reject the null hypothesis. In practical terms, this means that the mayor does not have sufficient statistical evidence to claim that the town's unemployment rate is lower than the national average.

It's important to note that a higher p-value suggests weaker evidence against the null hypothesis. In this case, with a p-value of 0.23, the result is not statistically significant at the 0.05 significance level. Therefore, the mayor should accept the null hypothesis and conclude that there is not enough evidence to support the claim that the town's unemployment rate is lower than the national average.