Answer:
H0: Having health insurance is independent of the size of the company.
Ha: Having health insurance is not independent of the size of the company.
χ²= 9.284
The corresponding p-value for the test is = 0.0096
Reject H0. We conclude health insurance coverage is not independent of the size of the company.
For small companies, 40% do not provide health insurance. For medium companies, 11.4% do not provide health insurance. For large companies,18 % do not provide health insurance.
These percentages support the conclusion that small companies are less more equally likely to provide health insurance coverage when compared to medium and large companies.
Step-by-step explanation:
small medium large Total
yes 30 59 82 171
no 20 16 18 54
Total: 50 75 100 225
Expected Values small medium large Total
yes { 50* 171/225} = 38 57 76 171
<u>no 12 18 24 54</u>
<u>Total 50 75 100 225 </u>
<u>Squared Distances small medium large</u>
yes {(30 - 38)^2}/38
= 1.684 0.07 0.474
no {(20 - 12)^2} /12
= 5.333 0.22 1.5
1) The null and alternative hypotheses can be formulated as
H0: Having health insurance is independent of the size of the company.
Ha: Having health insurance is not independent of the size of the company.
(2) the significance level is alpha =0.05 ,
the number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2df
so then the rejection region for this test is χ 2 :χ 2 >5.991.
3) Test Statistics under H0 is
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
4) χ²= 1.684+5.333+0.07+0.222+0.474+1.5
= 9.284
Since it is observed that χ²=9.284 >χ²= 5.991 it is concluded that the null hypothesis is rejected.
5) Conclusion
It is concluded that the null hypothesis H0 is rejected. Therefore, there is not enough evidence to claim that the two variables are dependent at 0.05 significance level.
The corresponding p-value for the test is = 0.0096
b) The percentages of
Small %= 20/50= 0.4= 40%
Medium %= 16/75 = 0.786= 11.4%
Large %= 18/100= 0.18= 18%
For small companies, 40% do not provide health insurance. For medium companies, 11.4% do not provide health insurance. For large companies,18 % do not provide health insurance.
These percentages support the conclusion that small companies are less more equally likely to provide health insurance coverage when compared to medium and large companies.
