Question: In this section, we assumed that the sample size was less than 5% of the size of the population. When sampling without replacement from a

In this section, we assumed that the sample size was less than 5% of the size of the population. When sampling without replacement from a ﬁnite population in which n > 0.05N, the standard deviation of the distribution of pn is given by

where N is the size of the population. A survey is conducted at a college having an enrollment of 6502 students. The student council wants to estimate the percentage of students in favor of establishing a student union. In a random sample of 500 students, it was determined that 410 were in favor of establishing a student union.

(a) Obtain the sample proportion, , of students surveyed who favor establishing a student union.

(b) Calculate the standard deviation of the sampling distribution of using as an estimate of p.

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