Suppose that 30% of female students and 25% of male students at a large high school are enrolled in an AP ® class. Independent r
andom samples of 20 females and 20 males are selected and asked if they are enrolled in an AP ® class. Let ˆ p F represent the sample proportion of females enrolled in an AP ® class and ˆ p F represent the sample proportion of males enrolled in an AP ® class. What is the mean of the sampling distribution of ˆ p F − ˆ p M ?
The mean of the sampling distribution of (ˆpF − ˆpM) = 0.05
Step-by-step explanation:
According to the central limit theorem, a sample extracted from a set of data is said to approximate a normal distribution with its sampling distribution having the same mean/proportion as the population mean/proportion.
Hence,
The sample proportion of females enrolled in an AP ® class = The population proportion of females enrolled in an AP ® class
ˆpF = 30% = 0.30
And the sample proportion of males enrolled in an AP ® class = The population proportion of males enrolled in an AP ® class
ˆpM = 25% = 0.25
So, the mean of the sampling distribution of (ˆpF − ˆpM) will simply be 30% - 25% = 5% = 0.05