Final answer:
The question pertains to hypothesis testing to determine if more than 80% of a town's population shops at Costco, using null and alternative hypotheses and the z-test for proportions.
Step-by-step explanation:
The student's question is about testing a hypothesis regarding a population proportion. Specifically, the hypothesis test is to determine if the proportion of all people in the town who shop at Costco is more than 80%.
Setting Up the Hypothesis Test
For hypothesis testing, we have two hypotheses:
- The null hypothesis (H0): This is the status quo and specifies that there is no effect or no difference. In this case, it would be H0: p ≤ 0.80, meaning the true population proportion of people who shop at Costco is less than or equal to 80%.
- The alternative hypothesis (Ha): This specifies what we are testing for. Here, it would be Ha: p > 0.80, indicating that the true population proportion is greater than 80%.
Performing the Test
To perform the test, we use a statistical test for proportions, often the z-test for proportions. We calculate the test statistic based on the difference between the sample proportion and the hypothesized proportion, and compare this to a critical value based on the significance level or find the p-value to determine if we reject or fail to reject the null hypothesis.
Conclusion
If the calculated p-value is less than the significance level (in this case, 0.1), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 80% of the town's population shops at Costco. If the p-value is greater than the significance level, we fail to reject the null hypothesis.