Question

Suppose that 40% of men over the age of 30 suffer from lower back pain. For a random sample of 50 men over the age of 30, find the mean and the standard error of the sampling distribution of the sample proportion of men over the age of 30 that suffer from lower back pain. What are Mean and Standard Error for the sample data?

Answer 1

Solution:

Population proportion of the men over the age of 30 who suffer from lower back pain is, P = 40% = 0.40

The mean of the sampling distribution of sample proportion is given by P and standard error is given by .

Where, P is population proportion, Q = 1 - P and n is sample size.

We have, P = 0.40, Q = 1 - 0.40 = 0.60 and n = 50

Hence, mean and the standard error of the sampling distribution of the sample proportion of men over the age of 30 that suffer from lower back pain is given as follows:

Mean = P = 0.40

The standard error is 0.06928.

Mean and standard error of sample data is as follows:

The mean of the sample data is 0.40 and standard error is 0.06928.