Question

Suppose public opinion is split 62% against and 38% for increasing taxes to help balance the federal budget. 320 people from the population are selected randomly and interviewed. The sampling distribution of the sample proportion of people who are in favor of increasing taxes to help balance the federal budget has a mean of and a standard deviation of__________

Answer 1

The mean of the sampling distribution of the sample proportion is 0.38. The standard deviation of the sampling distribution of the sample proportion is approximately 4.03%.

Step-by-step explanation:

The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is 38% or 0.38 in this case.

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

standard deviation = sqrt[(p(1-p))/n]

where p is the population proportion and n is the sample size.

Using the given information, the standard deviation of the sampling distribution of the sample proportion would be:

standard deviation = sqrt[(0.38(1-0.38))/320] ≈ 0.0403 or 4.03%