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 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.

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.

A

The expected cell counts are not large enough to apply the chi-square test for homogeneity.

The expected cell counts are not large enough to apply the chi-square test for homogeneity.

B

The total sample size is not large enough to apply the chi-square test for homogeneity.

The total sample size is not large enough to apply the chi-square test for homogeneity.

C

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

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

D

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

Transcribed Image Text: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 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. A В The expected cell counts are not large enough to apply the chi-square test for homogeneity. 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. All conditions necessary to apply the chi-square test for homogeneity are satisfied here.

Name: A manufacturing company with 350 employees is changing the employee he
Uploaded: 2024-03-20T07:06:41.000Z
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Description: 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 e

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 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.

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.

A
The expected cell counts are not large enough to apply the chi-square test for homogeneity.

The expected cell counts are not large enough to apply the chi-square test for homogeneity.

B
The total sample size is not large enough to apply the chi-square test for homogeneity.

The total sample size is not large enough to apply the chi-square test for homogeneity.

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

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

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

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 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.
A
В
The expected cell counts are not large enough to apply the chi-square test for homogeneity.
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.
All conditions necessary to apply the chi-square test for homogeneity are satisfied here.

Accepted Answer

The conditions for the chi-square test of homogeniety are-

The sample is a random sample
All…