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 463985Which 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.

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 463985Which 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.

Haiden Frazier · Accepted Answer

The conditions for the chi-square test of homogeniety are-1. The sample is a random sample2. All expected frequency from each of the cells are greater than 5.In the given question, the samples are selected randomly and each of the cells expected frequency is greater than 5. Therefore, option (e): &quot;All conditions necessary to apply chi-square test for homogeneity are satisfied here&quot; is the correct option.

A manufacturing company with 350 employees is changing the employee health insurance plan to either

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