In a large population, 55% get a physical examination at least once every two years. An SRS of 100 people are interviewed and the proportion of people who have had a physical is computed. What are the mean and standard deviation of the sampling distribution of the sample proportion?
A. 55,002
B. Can't determine the standard deviation from the information given
C. 0.55, 0.0497
D. 55, 2
Ε. 55, 4.97
C. 0.55, 0.0497
The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is 0.55 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 (0.55)
- n is the sample size (100)
Plugging in the values, we get:
Standard Deviation = sqrt( (0.55 * (1 - 0.55)) / 100)
Standard Deviation = sqrt(0.2475 / 100)
Standard Deviation = sqrt(0.002475)
Standard Deviation ≈ 0.0497
Therefore, the mean of the sampling distribution of the sample proportion is 0.55 and the standard deviation is approximately 0.0497.