The entire senior class of 2008 at Radford University (1800 students) decided to

Question

The entire senior class of 2008 at Radford University (1800 students) decided to take their Spring Break at for Lauderdale Beach. The organization Mothers Against Drunk Driving (MADD)decided to conduct a study on daily beer consumption among the RU senior class. In a similar study, researchers found that, on average, college students consume 12 cans of beer per person each day. Based on casual conversations with college students, MADD members found that while some spring break students do not drink any beer, others consumed as many as 21 cans per day.
What is the sample size if MADD wants to be 95% confident in its results and within +/- 1.5 cans of beer. (Please show work in detail). The entire senior class of 2008 at Radford University (1800 students) decided to take their Spring Break at for Lauderdale Beach. The organization Mothers Against Drunk Driving (MADD)decided to conduct a study on daily beer consumption among the RU senior class. In a similar study, researchers found that, on average, college students consume 12 cans of beer per person each day. Based on casual conversations with college students, MADD members found that while some spring break students do not drink any beer, others consumed as many as 21 cans per day.
What is the sample size if MADD wants to be 95% confident in its results and within +/- 1.5 cans of beer. (Please show work in detail). The entire senior class of 2008 at Radford University (1800 students) decided to take their Spring Break at for Lauderdale Beach. The organization Mothers Against Drunk Driving (MADD)decided to conduct a study on daily beer consumption among the RU senior class. In a similar study, researchers found that, on average, college students consume 12 cans of beer per person each day. Based on casual conversations with college students, MADD members found that while some spring break students do not drink any beer, others consumed as many as 21 cans per day.
What is the sample size if MADD wants to be 95% confident in its results and within +/- 1.5 cans of beer. (Please show work in detail).

Explanation / Answer

The standard deviation for this data set is:

S = (21-0)/6 = 3.5

This is calculated using the fact that more than 99% of the data lies with a span of six standard deviations:

3 deviations on either side of the mean.

The critical z-score for 95% CI for a two-sided test is:

zc = 1.96

Assuming S' denote the standard deviation of the sampling distribution.

So,

S'*zc = 1.5

Solving we get:

S' = 1.5/1.96 = 0.765

Also,

S' = S/(n)0.5

So,

3.5/(n)0.5 = 0.765

Solving we get:

n = 20.91

This value approximates 21.

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