Question

10% of all Americans suffer from sleep apnea. A researcher suspects that a different percentage or tiose Of the 359 people from the inner city surveyed, 43 of them suffered from steep apnea. Test the calim at who live in the inner city have sleep apnea. tevel of significance of α=0 Or10? a. What type of test should be run?

Answer 1

A researcher should use a two-tailed z-test for proportions to compare the observed proportion of sleep apnea in the inner city population to the general population, and test the claim at a significance level of 0.10.

Step-by-step explanation:

The question relates to a hypothesis test for a proportion. The type of test that should be run to determine if the proportion of those with sleep apnea in the inner city is different from the general population is a two-tailed z-test for proportions. This test is appropriate because we are comparing the observed proportion in the sample (43 out of 359 people) to the known proportion in the general population (10% or 0.10).

Here is how the hypothesis testing would be structured:

• Null Hypothesis (H0): The proportion of inner city residents with sleep apnea is equal to 0.10 (p = 0.10).
• Alternative Hypothesis (H1): The proportion of inner city residents with sleep apnea is not equal to 0.10 (p ≠ 0.10).

The significance level (α) is 0.10. The test statistic is calculated using the sample proportion and the standard error for the proportion. If the calculated z-score falls beyond the critical value for a significance level of 0.10, we reject the null hypothesis.