Question

Suppose a sample of 300 primary care doctors was taken. Calculate the mean and standard deviation of the sample proportion of doctors who think their patients receive unnecessary medical care.

Answer 1

The mean of the sample proportion of doctors who think their patients receive unnecessary medical care can be calculated using the formula
`\(\bar{p} = (x)/(n)\)`, where (x) is the number of doctors who think their patients receive unnecessary medical care, and (n) is the sample size. The standard deviation of the sample proportion
`(\(σ_{\bar{p}}\))` can be calculated using the formula
`\(σ_{\bar{p}} = \sqrt{(p(1-p))/(n)}\)`, where (p) is the estimated population proportion.

Step-by-step explanation:

To calculate the mean
`(\(\bar{p}\))`, you would sum up the number of doctors who think their patients receive unnecessary medical care (x) and then divide by the sample size (n). For example, if 100 doctors in the sample think their patients receive unnecessary medical care, and the sample size is 300, the mean
`(\(\bar{p}\))` would be
`\((100)/(300) = (1)/(3)\)`.

The standard deviation of the sample proportion
`(\(σ_{\bar{p}}\))` provides a measure of how spread out the sample proportion is around the true population proportion. It is calculated using the square root of the product of the estimated population proportion (p) and its complement
`(\(1-p\))`, divided by the sample size (n). For instance, if the estimated population proportion is 0.3 (30%), and the sample size is 300, the standard deviation
`(\(σ_{\bar{p}}\))` would be
`\(\sqrt{(0.3(1-0.3))/(300)}\)`.

In summary, the mean
`(\(\bar{p}\))` gives the central tendency of the sample proportion, while the standard deviation
`(\(σ_{\bar{p}}\))` provides a measure of its variability. These calculations are essential in understanding the distribution of opinions among primary care doctors regarding unnecessary medical care for their patients.