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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 Â Â Â Â Â Â Â Â 17 Â Â Â Â Â Â Â Â Â 10 Â Â Â Â Â Â Â Â Â Â 17 Â Â Â Â 57
high      7          15          15            10      47   Â
Total    30         65         57           53     205    Â
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    Â
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 Â Â Â Â Â Â 18.07 Â Â Â Â Â Â Â Â 15.85 Â Â Â Â Â Â 14.74 Â Â Â 57 Â
high      7.76        16.8          14.74       13.7     53       Â
Total    30.88      66.89        58.672      54.55     210.992 Â
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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