Answer:
Step-by-step explanation:
a. The hypothesis of testing are
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
The test statistics is calculated as
X² = <u>∑(Ei - Oi)²</u> ≅X²(r-1)(c-1)
i Ei
where Oi's are the observed values and Ei's are the expected values,
E= <u>row total × column total</u>
total
The expected values are
Sizeof the Company
Health Insurance Small Medium Large Total
Yes 42 63 84 189
No 8 12 16 36
Total 50 75 100 225
Therefore, the test statistics is
X² =∑ (<u>Ei -Oi)² </u>=6.94 ≅ x²₂
i Ei
The critical value is found to be 5.99. Since test statistics > critical value, we reject H0 and conclude that the health insurance coverage is not independent of the size of the company.
The associated p-value is 0.031 (<0.05).
b. Percentage of employees lacking health insurance coverage is
Small 14/50 x 100 = 28%
Medium 10/75 x 100 = 13%
Large 12/100 x 100 = 12%
Hence depending on the above percentage, we can support the claim that the employees of small companies are more likely to lack health insurance coverage.
