Question

Suppose that​ 30% of the female students and​ 40% of the male students in a college history class are from a major city. If there are 50 female students and 30 male students in the​ class, then ▼ of the female students and ▼ 15 14 13 12 of the male student are from a major city. Of the 80 students in the class in​ total, ▼ 34.65 33.75 32.85 36.25 ​% are from a major city. The percentage of students from a major city is not equal to the average of​ 30% and​ 40%, which is​ 35%, because the number of female and male students in the class ▼ is the same. differs.

Answer 1

Based on the above, the mean of the sampling distribution of ˆpF - ˆpM is 0.05.

What is the mean about?

There were 30% of female students and also 25% of male students at a large high school are said to beenrolled in an AP ® class.

Therefore, Independent random samples of 20 females and 20 males are collected and as such:

Using the central limit theorem, Sample proportion of females enrolled in an AP ® class is equal to the population proportion of females enrolled in an AP ® class

ˆpF = 30% = 0.30

The sample proportion of males enrolled in an AP ® class is equal to the population proportion of males enrolled in an AP ® class

ˆpM = 25% = 0.25

Therefore, the mean of the sampling distribution of ˆpF - ˆpM:

30% - 25% = 5%

= 0.05

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