Answer:
1. χ² = <u> 15.3902 </u>
2. The p value is :_____.a. less than .005
3. Conclusion
a. health insurance coverage is not independent of the size of the company
4. The percentages of employees
Small %= 33/50= 0.66
Medium %= 68/75 = 0.91
Large %= 88/100= 0.88
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: the employee health insurance coverage is independent of the size of the company
against the claim
Ha: the employee health insurance coverage is not independent of the size of the company
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
which has an approximate chi square distribution with ( 3-1) (2-1)= 2 d.f
4) Computations:
Under H0 , the observed frequencies are :
Observed Expected E (O-E) (O-E)² (O-E)²/E
33 42 -9 81 1.928
68 63 5 25 0.3968
88 84 4 16 0.1904
17 8 9 81 10.125
7 12 -5 21 1.75
<u>12 16 -4 16 1 </u>
<u> 15.3902 </u>
Expected Values are calculated using the formula :
Row Total * Column Total / sample size
E1= (33+17) (33+ 68+88)/ 50+75+100= 42
E4= (33+17) (17+ 7+ 12)/ 50+75+100=8
E2= (68+7) (33+ 68+88)/ 50+75+100= 63
E5= (68+7) (17+ 7+ 12)/ 50+75+100= 12
E3= (88+12) (33+ 68+88)/ 50+75+100= 84
E6= (88+12) (17+ 7+ 12)/ 50+75+100= 16
5) The critical region is χ² ≥ χ² (0.05)2 = 5.99
6) Conclusion:
The calculated χ² = <u> 15.3902 </u>falls in the critical region χ² ≥ 5.99 so we reject the null hypothesis that the employee health insurance coverage is NOT independent of the size of the company.
2. The p value is :_____.
a. less than .005
The p-value is .000385.
3. Conclusion
a. health insurance coverage is not independent of the size of the company
4. The percentages of employees
Small %= 33/50= 0.66
Medium %= 68/75 = 0.91
Large %= 88/100= 0.88
