Question

18.

1. Major health studies try very hard to select a sample that is representative of the various ethnic groups making up the U.S. population. Here is the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea:

White	Hispanic	African American	Asian/Pacific	Native American	Total
4821	277	510	88	598	6294

The known ethnic distribution in the United States, according to census data, is as follows:

White	Hispanic	African American	Asian/Pacific	Native American	Total
0.756	0.091	0.108	0.038	0.007	1

We want to know if the data from the sleep apnea study support the claim that the ethnicity of the subjects fits the ethnic composition of the U.S. population. What does the null hypothesis for this test state?

1. All five counts are equal.
2. All five sample proportions are equal.
3. All five population proportions are equal.
4. All five population proportions are equal to their respective U.S. census proportions.

2. For problem 18, What is the expected count of Hispanics under the null hypothesis (show calculation)?

1. 277
2. 25.207
3. 572.754
4. 152.72

3. For problem 18, software gives a chi-square statistic χ² = 7256.21 for these data. What is the P-value for this test?

1. Greater than 0.05
2. Less than 0.05 but greater than 0.01
3. Less than 0.01 but greater than 0.001
4. Less than 0.001

4. For problem 18, at significance level alpha = 1%, what should you conclude?

1. composition of the U.S. population.
2. The data are consistent with a uniform distribution of ethnicities.
3. The data prove that the population studied matches the ethnic composition of the U.S. population.
4. We are unable to conclude anything because the test assumptions are not met.

Answer 1