(a) A sample of the weekly earningsrecord of 12 production employees of Company
ID: 2918729 • Letter: #
Question
(a) A sample of the weekly earningsrecord of 12 production employees of Company A has a variance ofRs. 15.90 while a similar sample of 15 records for company Bemployees has a variance of Rs. 7.50. Is it safe to assume thatthere is less variance in the first population than in the second?Use the significance level of 0.05.
(b )To test the significance of variation inthe retail prices of a commodity in three principal cities,Faisalabad, Sialkot, and Gujranwala; four shops were chosen atrandom in each city and data is shown in the given table. Do thedata indicate that the prices in three cities are significantlydifferent? Complete the ANOVA table and draw your conclusion?
Sources of variation
d. f
Sums of Squares
Mean squares
F-ratios
Between samples
2
25
Within samples
86
Total
11
136
Sources of variation
d. f
Sums of Squares
Mean squares
F-ratios
Between samples
2
25
Within samples
86
Total
11
136
Explanation / Answer
Sources of variation
d. f
Sums of Squares
Mean squares
F-ratios
Between samples
2
25
Within samples
86
Total
11
136
Thus, the value of test statistic is F = 2.6162
Critical value of F:
At a = 0.05 level of significance,for V = (2, 9) degrees of freedom, the critical value of F is givenby
F0.05, (2, 9) =4.2565 (By referring F-distribution table)
State your decision regarding the null hypothesis.
If the value of test statistic is greater than the critical valueof F, then the null hypothesis is rejected. Otherwise the nullhypothesis is not rejected.
In this problem, since the value oftest statistic (2.6162) is less than the criticalvalue of F (4.2565), there is no enough evidenceto reject the null hypothesis H0 at 5% level. The threecities are not significantly different
Sources of variation
d. f
Sums of Squares
Mean squares
F-ratios
Between samples
2
5025
2.6162Within samples
986
9.5556Total
11
136
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