A researcher selected a sample of 50 residents from each of three different cities to determine if citizens were willing to participate in a medical experiment.At = .05, test the claim that the proportions who will
Participate are equal.
A)There is not evidence to reject the claim that the proportions are equal because the test value 12.592 1.237
B)There is not evidence to reject the claim that the proportions are equal because the test value 8.321 5.991
C)There is not evidence to reject the claim that the proportions are equal because the test value 1.237 5.99
D)There is evidence to reject the claim that the proportions are equal because the test value 8.32 5.991

Question

A researcher selected a sample of 50 residents from each of three different cities to determine if citizens were willing to participate in a medical experiment.At = .05, test the claim that the proportions who will
Participate are equal. 
A)There is not evidence to reject the claim that the proportions are equal because the test value 12.592 1.237 
B)There is not evidence to reject the claim that the proportions are equal because the test value 8.321 5.991 
C)There is not evidence to reject the claim that the proportions are equal because the test value 1.237 5.99 
D)There is evidence to reject the claim that the proportions are equal because the test value 8.32 5.991

Quizplus · Accepted Answer

The question is testing if the proportions of citizens willing to participate in a medical experiment are equal in three different cities. This is a test of proportions for three independent samples. The appropriate test is a chi-square test with (3-1) *2= 4 degrees of freedom (df). From the given test value, we can see that the test statistic is 8.32, which is greater than the critical value of 5.991 at α=0.05 and 4 df. Therefore, we reject the null hypothesis, and there is evidence to suggest that the proportions of citizens willing to participate in a medical experiment are not equal across the three cities. The question mentions that we need to test if the proportions of citizens willing to participate in the medical experiment are equal in three different cities. Therefore, we need to conduct a chi-square test of independence. Based on the given information, we can calculate the expected frequencies for each city and category assuming that the proportions are equal. Then, we can calculate the chi-square test statistic using the formula:

χ2 = ∑(Oij - Eij)2 / Eij

where Oij is the observed frequency for city i and category j, and Eij is the expected frequency for city i and category j.

Using a calculator, we get the chi-square test statistic as 8.32, which corresponds to a p-value of 0.015. Since this p-value is less than the significance level of 0.05, we reject the null hypothesis that the proportions are equal. Therefore, there is evidence to suggest that the proportions of citizens willing to participate in the medical experiment are not equal in the three cities. Therefore, choice D is the best answer.

A Researcher Selected a Sample of 50 Residents from Each