ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A Q.NO. 12

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

Question 12

A company used three different methods to train its employees. The number of units of output produced by different employees trained by the three training methods are given below:

• Method A: 50, 45, 55, 44

• Method B: 64, 48, 52, 56, 44

• Method C: 46, 42, 48, 45, 57, 42

The estimate of the population variance on the basis of the variance among the sample means for the above methods is:

(a) 45.25(b) 48.36(c) 52.58(d) 55.65

Answer

This question asks for the estimate of population variance based on variation among sample means, that is, the between-sample variance estimate in one-way ANOVA.

Step 1: Sample totals and sizes

For Method A:

T1 = 50 + 45 + 55 + 44 = 194, n1 = 4

For Method B:

T2 = 64 + 48 + 52 + 56 + 44 = 264, n2 = 5

For Method C:

T3 = 46 + 42 + 48 + 45 + 57 + 42 = 280, n3 = 6

Total number of observations:

N = 4 + 5 + 6 = 15

Grand total:

T = 194 + 264 + 280 = 738

Step 2: Correction factor

C.F. = T² / N = 738² / 15 = 36309.6

Step 3: Sum of squares between samples

SSB = (T1²/n1 + T2²/n2 + T3²/n3) − C.F.

= (194²/4 + 264²/5 + 280²/6) − 36309.6

= (9409 + 13939.2 + 13066.67) − 36309.6

= 105.27

Step 4: Mean square between samples

Degrees of freedom between samples:

k − 1 = 3 − 1 = 2

So,

MSB = SSB / 2 = 105.27 / 2 = 52.635

Therefore, the estimate of population variance based on variance among sample means is approximately:

52.58

Final Answer:

(c) 52.58

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

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