Question

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

a. 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.

b. What is the expected count of Hispanics under the null hypothesis (show calculation)?

a. 277

b. 25.207

c. 572.754

d. 152.72

c. At significance level alpha = 1%, what should you conclude

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

Answer 1

1.Here we have given sample proportion

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

2.Here it is population proportion from US census data.

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

Question A.

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?

answer:- option(d)

" All five population proportions are equal to their respective U.S. census proportions. "

Since,it is equivalent to check sample proportions equal with the population proportions

Question B

What is the expected count of Hispanics under the null hypothesis?

Answer:-

Expected count will be = Population proportion for Hispanic * Sample Total

= 0.091 * 6294 = 572.754

Hence Option (C) is correct

Question C

At significance level alpha = 1%, what can we conclude?

Answer:-

The figure in the above question is showng that " Proportion of Hispanic in the U S population "

So at 0.01 we can conclude that the original population proportion for the Hispanic ethnic group is 572.754 > 277.

Hence we dont have evidence to say that it is same at 0.01.

Hence it is the "composition of the U.S. population." option(a) is correct.