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Sagot :
Answer:
As the calculated χ² = 1.23 is less than the critical region χ²≥ χ²(0.05,9)= 16.92 ,Staples can conclude that demands for these two types of computers are independent at the 0.05 level of significance.
Step-by-step explanation:
As we have to test the independence of the two categories the chi square of independence test is applied.
Let the null and alternate hypotheses be
H0 :The demand for each type of computers is independent
against the claim
Ha: The demand for each type of computers is not independent i.e they are associated.
The significance level alpha is chosen to be 0.05
The critical region for alpha =0.05 and (4-1)(4-1) = 3*3 =9 d.f is
χ²≥ χ²(0.05,9)= 16.92
Actual Data
low med-low med-high high Total
low 4 15 14 3 36
med-low 6 18 18 23 65
med-high 13 17 10 17 57
high 7 15 15 10 47
Total 30 65 57 53 205
Expected Frequencies
low- low = 30*36/205= 5.27
low- med.low = 65*36/205 = 11.41
low- medium high = 57*36/205= 10.009
low- high = 53*36/205 =9.31
medium low- low = 30*65/205 = 9.51
medium low- med.low = 65*65/205= 20.61
medium low- medium high = 57*65/205= 18.073
medium low- high = 53*65/205= 16.80
medium high- low = 30*57/205= 8.34
medium high- med.low = 65*57/205= 18.07
medium high- medium high = 57*57/205= 15.85
medium high- high = 53*57/205= 14.74
high- low = 30*53/205= 7.76
high- med.low = 65*53/205= 16.80
high- medium high = 57*53/205= 14.74
high- high = 53*53/205= 13.70
Summarizing in a table
Expected Frequencies
low med-low med-high high Total
low 5.27 11.41 10.009 9.31 35.999
med-low 9.51 20.61 18.073 16.8 64.993
med-high 8.34 18.07 15.85 14.74 57
high 7.76 16.8 14.74 13.7 53
Total 30.88 66.89 58.672 54.55 210.992
Using Excel
The Chi Square Values are
0.062823
0.270857
0.159572
0.735995791
1.229247532
As the calculated χ² = 1.23 is less than the critical region χ²≥ χ²(0.05,9)= 16.92 ,Staples can conclude that demands for these two types of computers are independent at the 0.05 level of significance,
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