Final answer:
To investigate if inner-city kindergarten children are more likely to have asthma than those in the suburbs at the 0.01 significance level, we conduct a hypothesis test comparing the proportions using a chi-square test. The null hypothesis assumes equal proportions, and we look for evidence to reject this in favor of a higher proportion of asthma cases among inner-city children.
Step-by-step explanation:
To test the claim that inner-city children are more likely to have asthma than children who live in the suburbs at the 0.01 level of significance, we are looking to conduct a hypothesis test. Here, we will compare two proportions: the proportion of children diagnosed with asthma in the suburbs (24 out of 415) and the proportion in the inner city (69 out of 638). We use a chi-square test for the difference between two proportions in this scenario.
The hypotheses for this test will be:
- Null Hypothesis (H0): p1 = p2, where p1 is the proportion of suburban children with asthma, and p2 is the proportion of inner-city children with asthma.
- Alternative Hypothesis (H1): p1 < p2, suggesting that the proportion of inner-city children with asthma is greater than the proportion of suburban children with asthma.
A Z-test can be used to determine if the difference observed is statistically significant. We will calculate the z-value and compare it to the critical value for the 0.01 level of significance or look up the corresponding p-value. If the calculated p-value is less than the significance level, we reject the null hypothesis, supporting the claim that inner-city children are more likely to have asthma.