Question

A sample of manufactured items will be selected from a large population in which 8 percent of the items are defective. of the following, which is the least value for a sample size that will allow for the sampling distribution of the sample proportion to be assumed approximately normal?

Answer 1

The sample size required should be at least of size 30.

According to the Central limit theorem, if from an unknown population large samples of sizes n ≥ 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\mu_{\hat p}=pμp^=p

The standard deviation of this sampling distribution of sample proportion is:

\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}σp^=np(1−p)

Here it is provided that manufactured items are selected from a large population in which 8% of the items are defective.

That is, the proportion of defective items is, p = 0.08.

For the sampling distribution of the sample proportion of defective items to be normally distributed the least sample size required is 30.

Thus, the sample size required should be at least of size 30.