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The following describes summary statistics for performance in examination of a random sample of 50 students from a population of 250 students of a certain school.

$$ \begin{array}{c|lcr} & \text{Passed in English} & \text{Failed in English} & \\ \hline \text{Passed in Maths} & 23 & 17 \\ \text{Failed in Maths} & 3 & 7 \\ \end{array} $$ (a) Find an estimate of the percentage of students failing in exactly one subject, and also find an unbiased estimate of its variance

(b) If it is further known that overall 202 students have passed in Mathematics, how will you modify the estimate of the percentage in (a) above?

I am a total newbie in sampling and any kind of help shall be appreciated.

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  • $\begingroup$ Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$
    – gung - Reinstate Monica
    Mar 31, 2018 at 17:56

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If simple random sampling without replacement has been employed to drawn the sample, then usual results apply: $\hat{p} = \frac{a}{n} $, where $a= 3+17 =20$ is the number of successes and $n=50$ is the sample size.

The variance estimator is $v(\hat{p}) = \frac{N-n}{N}\frac{\hat{p}(1-\hat{p})}{n-1}$

References

Cochran, W. G. (1977). Sampling Techniques: 3d Ed. Wiley.

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  • $\begingroup$ Please be cautious about providing complete answers to homework questions. Our policy is to provide hints only (see here). $\endgroup$
    – gung - Reinstate Monica
    Mar 31, 2018 at 17:58
  • $\begingroup$ @gung Its a one liner answer and plus as i have said , that this is the first time i m seeing this kind of question $\endgroup$
    – DRPR
    Mar 31, 2018 at 18:07
  • $\begingroup$ It's OK. My comment is for future reference. The point is to provide hints, not do their HW for them, no matter how simple the question seems. $\endgroup$
    – gung - Reinstate Monica
    Mar 31, 2018 at 18:19
  • $\begingroup$ @gung You're right, I didn't see the [self-study] tag so I didn't think of it. Thank you. $\endgroup$
    – Roberto
    Mar 31, 2018 at 18:28

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