A company compiles data on a variety of issues in education. In 2000 the company

Question

A company compiles data on a variety of issues in education. In 2000 the company reported that the national college freshman-to-sophomore retention rate was 72%. Consider colleges with freshman classes of 800 students. Use the 68-95-99.7 rule to describe the sampling distribution model for the percentage of students expected to return for their sophomore years. Do you think the appropriate conditions are met? Which graph shows the distribution of the proportion with the intervals for 68%, 95%, and 99.7%? Are the conditions necessary to use a normal model met? A. Yes, all the conditions are met. B No, the success/failure condition is not met. C No, the randomization and success/failure conditions are not met. D No, the 10% condition is not met. No, the randomization and 10% conditions are not met. F No, the 10% and success/failure conditions are not met. G No, the randomization condition is not met. H No, none of the conditions are met.

Explanation / Answer

The sampling distribution for the percentage of students expected to return for their sophomore years is approximately normal with mean same as population proportion p^=0.72 and standard deviation root over (p*(1-p)/n)=sq rt(0.72*0.28/800)=0.02

The graph A represents the distribution of proportions with the intervals for 68%,95%,99.7% as mu=0.72,mu+2sigma=0.72+2*0.02=0.76,mu+3*sigma=0.78,mu-3sigma=0.66

The sample considers a whole population of freshman classes. Thus the sample is not a simple random sample so the randomization condition is not met.

Since np=0.72*0.800=576, the 10% conditions are met.

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