Question

In a large population, 81% of the households have cable tv. A simple random sample of 196 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

0.028

Explanation:

Given that :

Population = Large

Household with cable TV = 81%

Sample size (n) = 196

The mean of sampling distribution (μx) = p = 81% = 81/100 = 0.81

The standard deviation of sampling distribution

Standard deviation (σ) :

σ = √[(p*(1 - p)) / n]

= √(0.81 * (1 - 0.81)) / 196

= √(0.1539 / 196)

= √0.0007852

= 0.0280214

= 0.028