ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A Q.NO. 13

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

Question 13

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, 44Method B: 64, 48, 52, 56, 44Method C: 46, 42, 48, 45, 57, 42

The estimate of the population variance within the samples for the different methods is:

(a) 25.67 (b) 31.07 (c) 38.646 (d) 39.097

Solution

This question asks for Mean Square Error (MSE), i.e., Estimate of population variance within samples

Step 1: Compute ΣX²

For Method A:

50² + 45² + 55² + 44²= 2500 + 2025 + 3025 + 1936= 9486

For Method B:

64² + 48² + 52² + 56² + 44²= 4096 + 2304 + 2704 + 3136 + 1936= 14176

For Method C:

46² + 42² + 48² + 45² + 57² + 42²= 2116 + 1764 + 2304 + 2025 + 3249 + 1764= 13222

Total:

ΣX² = 9486 + 14176 + 13222ΣX² = 36884

Step 2: Correction Factor

T = 194 + 264 + 280 = 738

N = 15

C.F. = T² / N

C.F. = (738)² / 15

C.F. = 544644 / 15

C.F. = 36309.6

Step 3: Total Sum of Squares

SST = ΣX² − C.F.

SST = 36884 − 36309.6

SST = 574.4

Step 4: Sum of Squares Between Samples

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

SSB = (9409 + 13939.2 + 13066.67) − 36309.6

SSB = 105.27

Step 5: Sum of Squares Within Samples

SSE = SST − SSB

SSE = 574.4 − 105.27

SSE = 469.13

Step 6: Mean Square Within Samples

Degrees of freedom:

df = N − k = 15 − 3 = 12

MSE = SSE / df

MSE = 469.13 / 12

MSE = 39.094

≈ 39.097

Final Answer

(d) 39.097

Important Exam Insight

MSE represents: Estimate of population variance within samples (error variance)

In ANOVA:

• MSB → Between groups variance

• MSE → Within groups variance

ISS PREVIOUS YEAR 2016 PAPER-2 SOLUTION SET-A

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