Question

er 12 Assignment 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 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. No 34 16 Health Insurance Size of Company Yes Total Small Medium 66 Large 11 100 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 xạ test statistic (to 2 decimals). 9 75 89 14.46 The p-value is less than .005 Using a=.05 level of significance, what is your conclusion? Conclude 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 32 7 % % Medium Based on the percentages calculated above, what can you conclude?

Answer 1

The statistic software output for this problem is:

Contingency table results: Rows: var1 Columns: None Yes No Total Small 34 16 50 Medium 66 9 75 Large 89 11 100 Total 189 36 225 Chi-Square test: Statistic DF Value P-value Chi-square 2 12.276786 0.0022

(a)

$\chi^2$ = 12.28

The p-value is 0.0022

b)

Small 16 / 50 = 32%

Medium 9 / 75 = 12%

Large 11 / 100 = 11%