Question

Suppose that 30% of female students and 25% of male students at a large high school are enrolled in an AP ® class. Independent random 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 ?

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

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

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