Answer:
The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent
The p-value is 0 .001909. The result is significant at p < 0.05
Part b:
40 > 8.5
35> 7.5
25> 4
Explanation:
1) Let the null and alternative hypothesis as
H0: the quality of management and the reputation of the company are independent
against the claim
Ha: the quality of management and the reputation of the company are dependent
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) (3-1)= 4 d.f
4) Computations:
Under H0 ,
Observed Expected E χ²= ∑(O-e)²/e
40 35.00 0.71
25 24.50 0.01
5 10.50 2.88
35 40.00 0.62
35 28.0 1.75
10 12.00 0.33
25 25.00 0.00
10 17.50 3.21
15 7.50 7.50
∑ 17.0281
Column Totals 100 70 30 200 (Grand Total)
5) The critical region is χ² ≥ χ² (0.05)2 = 9.49
6) Conclusion:
The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent.
7) The p-value is 0 .001909. The result is significant at p < 0.05
The p- values tells that the variables are dependent.
Part b:
If we take the excellent row total = 70 and compare it with the excellent column total= 100
If we take the good row total = 70 and compare it with the good column total= 80
If we take the fair row total = 50 and compare it with the fair column total= 30
The two attributes are said to be associated if
Thus we see that ( where (A)(B) are row and columns totals and AB are the cell contents)
AB> (A)(B)/N
40 > 1700/200
40 > 8.5
35> 1500/200
35> 7.5
25> 800/200
25> 4
and so on.
Hence they are positively associated