Of the 36 accounts drawn randomly from a very large number of...

ICAR JRF Computer Application 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

Of the 36 accounts drawn randomly from a very large number of accounts in a certain bank, 12 had a deposit of less than Rs. 1500. The estimated standard error for the estimate of the proportion of accounts having a deposit of less than Rs. 1500 is

2105 21315 2 [2 : on Correct

Standard Error of Estimated Proportion:
Sample size: $n = 36$
Number of accounts with deposit < Rs. 1500: $x = 12$
Sample proportion: $p = \frac{x}{n} = \frac{12}{36} = \frac{1}{3}$, and $q = 1 - p = \frac{2}{3}$
In simple random sampling from a very large population, the unbiased estimator of the variance of the sample proportion is:

$$s_p^2 = \frac{p(1 - p)}{n - 1} = \frac{\frac{1}{3} \times \frac{2}{3}}{36 - 1} = \frac{2/9}{35} = \frac{2}{315}$$

The estimated standard error ($SE$) is the square root of the variance:

$$SE(p) = \sqrt{\frac{p(1 - p)}{n - 1}} = \sqrt{\frac{2}{315}}$$

Conclusion: The estimated standard error is $\sqrt{\frac{2}{315}}$ (Option 4).

Correct option: (4) on

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