Question

A manufacturing company with 350 employees is changing the employee health insurance plan to either plan A or plan B. The company wants to know if employees have a preference between the two plans and whether or not preference differs between those employees who have family members covered under the current plan (group 1) and those who do not (group 2). The human resources office takes a simple random sample from each of the two groups, sends information about both plans to the employees in each sample, and asks them whether they prefer plan A or plan B. The table summarizes the responses received, with expected cell counts in parentheses.
Plan A Plan B Total
Yes (group 1) 40 (32.5) 20 (27.5) 60
No (group 2) 6 (13.5) 19 (11.5) 25
Total 46 39 85

Which statement is true about whether the conditions for the chi-square test for homogeneity have been met?
a. A simple random sample should have been taken from all the employees, and then each employee in the sample should have been asked their plan preference and whether or not they have family members covered under the current health insurance plan.
b. The expected cell counts are not large enough to apply the chi-square test for homogeneity.
c. The total sample size is not large enough to apply the chi-square test for homogeneity.
d. The total sample size is too large to apply the chi-square test for homogeneity.
e. All conditions necessary to apply the chi-square test for homogeneity are satisfied here.

Answer 1

Answer:

e. All conditions necessary to apply the chi-square test for homogeneity are satisfied here.

Step-by-step explanation:

The chi square statistic can also be used when the rows of the table which look like a contingency table represent each a different sample or set of observations. The hypothesis to be tested is that two or more different random samples come from the same population or that the samples are homogeneous . The χ² test  applied in this situation is called test of homogeneity.

The conditions for the chi square test of homogeneity are

1) the sample is a random sample

2) all expected counts are greater or equal to 5.

In the given question the sample selected are random samples and all the expected counts are greater than 5.

Also the 2 samples have been chosen from the same population and tested whether they have the same results or not.

Part e is the best option.

Answer 2

Answer: D. The total sample size is too large to apply the chi-square test for homogeneity.

Step-by-step explanation: When sampling without replacement, the sample size should not exceed 10 percent of the population size. Here, the sample size of 85 is just over 24 percent of the population of 350 company employees.