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- 4821 Hispanic-277 African American- 510 Asian/Pacific- 88 Native American- 598 Total- 6294 The known ethnic distribution in the United States, according to census data, is as follows: White-0.756 Hispanic- 0.091 African American- 0.108 Asian/Pacific- 0.038 Native American-0.007 Total-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? a. All five counts are equal. b. All five sample proportions are equal. c. All five population proportions are equal. d. All five population proportions are equal to their respective U.S. census proportions. 

What is the expected count of Hispanics under the null hypothesis (show calculation)? a. 277 b. 25.207 c. 572.754 d. 152.72 software gives a chi-square statistic χ2 = 7256.21 for these data. What is the P-value for this test? a. Greater than 0.05 b. Less than 0.05 but greater than 0.01 c. Less than 0.01 but greater than 0.001 d. Less than 0.001

at significance level alpha = 1%, what should you conclude? a. composition of the U.S. population. b. The data are consistent with a uniform distribution of ethnicities. c. The data prove that the population studied matches the ethnic composition of the U.S. population. d. We are unable to conclude anything because the test assumptions are not met.

Answer 1

The breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea and their corresponding probability is given.

The null hypothesis for this test state is that All five population proportions are equal to their respective U.S. census proportions.

Hence, option d is the correct answer.

Using the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea the total number of US population that are Hispanics is 277 and its corresponding probability is 0.091.

The expected count of Hispanics under the null hypothesis is calculated by multiplying the nuber of people in US population that are Hispanics with its corresponding probability and is given by:

Hence, the expected count of Hispanics under the null hypothesis is 25.207.

Hence, option b is the correct answer.

            The p-value is calculated from chi square calculator and is less than 0.001.

Hence, option d is the correct answer.

The null hypothesis for this test state is that all five population proportions are equal to their respective U.S. census proportions.

The null hypothesis for this test state is that all five population proportions are not equal to their respective U.S. census proportions that is at least one population proportion is different from its respective U.S census proportions.

The obtained p value is less than 0.001 which is also less than the significance level 0.01.

So, the decision is to reject the null hypothesis and conclude that that there is significant evidence that the population studied does not match the ethnic composition of the American population.