Health insurance benefits 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 employees. Medium-sized companies have to employees, and large companies have or more employees. The questionnaire sent to 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 YesNo Total   Small341650  Medium70575  Large8515100  a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the -value?Compute the value of the test statistic (to 2 decimals). The -value is - Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Using level of significance, what is your conclusion?- Select your answer -Cannot reject the assumption that health insurance coverage and size of the company are independentConclude health insurance coverage is not independent of the size of the companyb. 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  Based on the percentages calculated above, what can you conclude?- Select your answer -Large companies have a higher percentage of no coverage than medium and small companiesMedium companies have a higher percentage of no coverage than large and small companiesSmall, medium, and large companies all have roughly the same percentage of no coverageSmall companies have a higher percentage of no coverage than large and medium companies

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Asked Jan 1, 2020
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Health insurance benefits 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 employees. Medium-sized companies have to employees, and large companies have or more employees. The questionnaire sent to 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 34 16 50  
  Medium 70 5 75  
  Large 85 15 100  

 

a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the -value?

Compute the value of the test statistic (to 2 decimals).

 

The -value is - Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10

Using level of significance, what is your conclusion?

- Select your answer -Cannot reject the assumption that health insurance coverage and size of the company are independentConclude health insurance coverage is not independent of the size of the company

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  

 

Based on the percentages calculated above, what can you conclude?

- Select your answer -

Large companies have a higher percentage of no coverage than medium and small companies

Medium companies have a higher percentage of no coverage than large and small companies

Small, medium, and large companies all have roughly the same percentage of no coverage

Small companies have a higher percentage of no coverage than large and medium companies

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Expert Answer

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Step 1

a:

For the given data, the chi-square test for association is appropriate.

Null Hypothesis:

H0: The health insurance coverage is independent of the size of the company.

Alternative Hypothesis:

H1: The health insurance coverage is not independent of the size of the company.

Chi-square test is appropriate in this situation.

Decision rule:

If p-value ≤ α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.

Procedure for calculating chi-square test statistic using MegaStat:

  • Go to MegaStat > Chi-square/Crosstab > Contingency table.
  • Select the input range of the data as “$A$1:$C$4”.
  • In output options, Select expected values, Chi-square and (O-E)2/E.
  • Click ok.

From the MegaStat output, the chi-square test statistic is 14.46  which is given below:

 

Statistics homework question answer, step 1, image 1
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Step 2

From the output,

Chi-square is 14.46.

Degree of freedom is 2.

The p-value is 0.0007. The p-value is less than 0.005.

Assume the level of significance is 0.05.

Here, p-value is 0.0007, which is less than the level of significance (0.05). Thus, reject the null hypothesis. Thus, it can be conclude that health insurance coverage is not independent of the size of the company.

Step 3

b)

The percentages of employees without health insurance based...

Statistics homework question answer, step 3, image 1
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