Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For 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 1,000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company. Size of the Company Health Insurance Small Medium Large Yes 33 62 85 No 17 13 15 (a) Perform a test of independence to determine health insurance coverage is related to the size of the company. State the null and alternative hypotheses. Ho: Having health insurance is not independent of the size of the company. H: The proportion of companies with health insurance benefits is not equal for small, medium and large companies. O Ho: Having health insurance is independent of the size of the company. H: The proportion of companies with health insurance benefits is equal for small, medium and large companies. O Ho: Having health insurance is not independent of the size of the company. H: Having health insurance is independent of the size of the company. O Ho: Having health insurance is independent of the size of the company. H: Having health insurance is not independent of the size of the company. Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = Using a 0.05 level of significance, what is your conclusion? O Reject Ho. We conclude health insurance coverage is independent of the size of the company. Do not reject Ho. We cannot conclude health insurance coverage and the size of the company are not independent. O Do not reject Ho. We cannot conclude health insurance coverage is independent of the size of the company. O Reject Ho. We conclude health insurance coverage is not independent of the size of the company.
Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For 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 1,000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company. Size of the Company Health Insurance Small Medium Large Yes 33 62 85 No 17 13 15 (a) Perform a test of independence to determine health insurance coverage is related to the size of the company. State the null and alternative hypotheses. Ho: Having health insurance is not independent of the size of the company. H: The proportion of companies with health insurance benefits is not equal for small, medium and large companies. O Ho: Having health insurance is independent of the size of the company. H: The proportion of companies with health insurance benefits is equal for small, medium and large companies. O Ho: Having health insurance is not independent of the size of the company. H: Having health insurance is independent of the size of the company. O Ho: Having health insurance is independent of the size of the company. H: Having health insurance is not independent of the size of the company. Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = Using a 0.05 level of significance, what is your conclusion? O Reject Ho. We conclude health insurance coverage is independent of the size of the company. Do not reject Ho. We cannot conclude health insurance coverage and the size of the company are not independent. O Do not reject Ho. We cannot conclude health insurance coverage is independent of the size of the company. O Reject Ho. We conclude health insurance coverage is not independent of the size of the company.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:(b) A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the above data to support this conclusion. (Round your
answers to the nearest integer.)
For small companies,
% do not provide health insurance. For medium companies,
% do not provide health insurance. For large companies,
% do
not provide health insurance. These percentages support the conclusion that small companies are
---Select---
O likely to provide health insurance coverage when compared to medium and
large companies.
Transcribed Image Text:Health insurance benefits vary by the size of the company. The sample data below show the number of companies providing health insurance for small, medium, and large companies. For 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 1,000 or more employees.
The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company.
Size of the Company
Health Insurance
Small
Medium
Large
Yes
33
62
85
No
17
13
15
(a) Perform a test of independence to determine if health insurance coverage is related to the size of the company.
State the null and alternative hypotheses.
Ho: Having health insurance is not independent of the size of the company.
H: The proportion of companies with health insurance benefits is not equal for small, medium and large companies.
Ho: Having health insurance is independent of the size of the company.
H3:
: The proportion of companies with health insurance benefits is equal for small, medium and large companies.
Ho: Having health insurance is not independent of the size of the company.
H: Having health insurance is independent of the size
company.
Ho: Having health insurance is independent of the size of the company.
H: Having health insurance is not independent of the size of the company.
Find the value of the test statistic. (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value
%3D
Using a 0.05 level of significance, what is your conclusion?
Reject Ho. We conclude health insurance coverage is independent of the size of the company.
Do not reject Ho. We cannot conclude health insurance coverage and the size of the company are not independent.
Do not reject Ho: We cannot conclude health insurance coverage is independent of the size of the company.
Reject Ho. We conclude health insurance coverage is not independent of the size of the company.
Expert Solution
Step 1:-
Hypothesis,
Option (a) is right.
Here we use Chi-square Statistic.
We know,
Chi square= summation (Oi-Ei)2/Ei
Where Eis are expected Frequencies abd Oi's are observed values.
So to Calculate Chi-square we Calculate Expected values.
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