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According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduates from public universities had student loans. We randomly sample college graduates from public universities and determine the proportion in the sample with student loans. For which of the following sample sizes is a normal model a good fit for the sampling distribution of sample proportions?

A. 10
B. 20
C. 30
D. both 20 and 30
E. none of these

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Answer:

C. 30

Step-by-step explanation:

-It is a statistical rule of thumb  that the size of a sample must be [tex]n\geq 30[/tex].

-This size is deemed adequate for the Central Limit Theorem to hold.

-At this size or greater, the shape of the resultant distribution is normal.

#It should however be noted, that for a normal distribution the CLT holds even for smaller sample sizes.

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