Final answer:
We are testing a hypothesis about a population proportion, specifically whether more than 31% of the population has mental health issues based on a sample proportion of 32%. The steps involve stating hypotheses, calculating a test statistic and p-value, comparing the p-value with the significance level, and stating a conclusion.
Step-by-step explanation:
The question asks us to test the claim that the proportion of people who have some types of mental health issues is greater than 31%. A sample of 800 people showed that 32% had a mental health issue, and we are to use a significance level of 7%. This is a hypothesis test for a proportion.
- State the null hypothesis (H0: p ≤ 0.31) and the alternative hypothesis (Ha: p > 0.31), where p represents the true population proportion.
- Calculate the test statistic using the sample proportion, the null hypothesis proportion, and the sample size.
- Determine the p-value associated with the test statistic.
- Compare the p-value with the significance level (α = 0.07). If the p-value is less than 0.07, we reject the null hypothesis.
- State the conclusion based on the decision to reject or not reject H0.
If the null hypothesis is rejected, it can be concluded that there is evidence to support the claim that more than 31% of the population has some types of mental health issues at the 7% significance level.