Health insurance benetits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company. Health Insurance Size of Company Yes No Total Small 40 10 50 Medium 63 12 75 Large 86 14 100 a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 5E
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Health insurance benetits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data
below show the number of companies providing health insurance for small, medium, and large companies. For the purposes of this study, small
companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have
1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the
enployee to indicate the size of the company.
Health Insurance
Size of Company
Yes
No
Total
Small
40
10
50
Medium
63
12
75
Large
86
14
100
a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-
value?
Compute the value of the x? test statistic (to 2 decimals).
The p-value is greater than .10
Using a = .05 level of significance, what is your conclusion?
Cannot reject the assumption that health insurance coverage and size of the company are independent
b. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of
employees without health insurance based on company size (to the nearest whole number).
Small
Medium
%
Large
Transcribed Image Text:Health insurance benetits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company. Health Insurance Size of Company Yes No Total Small 40 10 50 Medium 63 12 75 Large 86 14 100 a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p- value? Compute the value of the x? test statistic (to 2 decimals). The p-value is greater than .10 Using a = .05 level of significance, what is your conclusion? Cannot reject the assumption that health insurance coverage and size of the company are independent b. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number). Small Medium % Large
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