Question

A survey was conducted in a slum locality of 2000 families by selecting a sample of size 800. It was revealed that 180 families were illiterates. Find the probable limits of the illiterate families in the population of 2000.

Answer 1

Answer on Question #46082 – Math – Statistics and Probability

A survey was conducted in a slum locality of 2000 families by selecting a sample of size $n = 800$. It was revealed that 180 families were illiterates. Find the probable limits of the illiterate families in the population of $N = 2000$.

Solution

The level of significance is not given. Then we can use $3\sigma$-limits. Hence, the probable limits for the proportion in the population are:

$$p \pm 3\sigma = p \pm 3\sqrt{\frac{pq}{n}}.$$

The probable limits of the illiterate families in the population of $N = 2000$ are

$$N\left(p \pm 3\sqrt{\frac{pq}{n}}\right) = 2000\left(\frac{180}{800} \pm 3\sqrt{\frac{\frac{180}{800}(1 - \frac{180}{800})}{800}}\right) = 2000(0.225 \pm 3 \cdot 0.015) = 2000(0.225 \pm 0.045) = (360; 540).$$

Answer: (360; 540).

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