Question

eBook 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 Health Insurance Size of Company Yes Total Small 38 50 Medium 63 12 Large 88 12 100 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). 5.94 * The p-value is between .005 and .01 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 32 13 12 % % % Based on the percentages calculated above, what can you conclude? Small companies have a higher percentage of no coverage than large and medium companies

Answer 1

(a) Excel add-in (Mega Stat) procedure: Step 1: In EXCEL, Select Add-Ins > Mega Stat> Chi-square/Crosstab > Contingency Table. Step 2: In Input range, select the cell range Al:C4 Step 3: In Output Options, select chi-square and % of row Step 4: Click OK Excel add-in (Mega Stat) output:

Chi-square Contingency Table Test for Independence No 12 24.0% 12 16.0% Yes 38 Total Small Observed % of row Medium Observed % of row Large Observed % of row Observed 50 100.0% 75 100.0% 100 100.0% 225 76.0% 63 84.0% 88 12 88.0% 12.0% Total 189 36 % of row 84.0% 16.0% 100.0% 3.57 chi-square 2 df 1677 p-value The value oftest statistic is 3.57 The p-value is between 0.10 and 0.20 (b) Small 24% Medium 16 % Large 12%