Question

In a large population, 67% of the households have cable tv. A simple random sample of 64 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions?

Answer 1

The mean of the sampling distribution of the sample proportions is the same as the population proportion, which is 0.67.

The standard deviation of the sampling distribution of the sample proportions can be calculated using the formula:

σp = sqrt [p * (1 - p) / n]

where p is the population proportion (0.67), n is the sample size (64), and σp is the standard deviation of the sampling distribution of the sample proportions.

Plugging in the values, we get:

σp = sqrt [0.67 * (1 - 0.67) / 64]

= sqrt [0.2211 / 64]

= 0.061

Therefore, the standard deviation of the sampling distribution of the sample proportions is 0.061.