Answer:
The calculated χ² = 21.455 falls in the critical region χ² ≥ 7.815 so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.
Explanation:
1) We set up our null and alternative hypothesis as
H0: the type of hard drive and the store where the computers were bought are dependent
against the claim
Ha: the type of hard drive and the store where the computers were bought are independent
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 ( 4-1) (2-1)= 3 d.f
4) Computations:
Using the calculator we summarize the results as
Under H0 , the observed frequencies are :
Observed Expected E χ²= (O-E)²/E
13 (23.58) [4.75]
11 (10.63) [0.013]
19 (14.69) [1.264]
9 (3.09) [11.282]
109 (98.42) [1.138]
44 (44.37) [0.003]
57 (61.31) [0.303]
7 (12.91) [2.703]
∑ 21.455
5) Conclusion:
The calculated χ² = 21.455 falls in the critical region χ² ≥ 7.815 so we reject the null hypothesis that the type of hard drive and the store where the computers were bought are dependent and accept the claim the type of hard drive and the store where the computers were bought are independent.
The p-value is .000085.
The result is significant at p < .05 meaning the claim is accepted.