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(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

50

25

2.6162

Within samples

9

86

9.5556

Total

11

136