1. What important role does the central limit theorem serve whenever is used to estimate m ? (15 points)

 

 

 

2. The starting salary of a college graduate is considered a random variable x. What is the difference between the probability distribution of x and the probability distribution of , the sampling distribution? (10 points)

 

 

 

 

 

 

3. The student population of Hanover College has a mean age of 20.243 years with a standard deviation of 1.0407 years.

1. Show the sampling distribution of . (5 points)

 

 

 

2. What is the standard deviation of ? (5 points)

 

3. What is the probability that the sample mean for a sample of 50 students will be over the age of 20.5 years? (5 points)

1. A random sample of 120 Hanover College undergraduates were asked if they were a member of a Greek organization, or not. Below are some descriptive statistics for this variable. Please interpret the meaning of the result in the last row, the "Confidence Level (95%)". (10 points)

GREEK
Mean	0.583333333
Standard Error	0.045193845
Median	1
Mode	1
Standard Deviation	0.495073771
Sample Variance	0.245098039
Count	120
Confidence Level(95.0%)	0.089488211

2. The Tourism Institute for the State of Florida plans to sample visitors at major beaches throughout the state to estimate the proportion of beach visitors who are not residents of Florida. Preliminary estimates are that 55% of the beach visitors are not Florida residents.

1. How large a sample should be taken to estimate the proportion of out-of-state visitors to within ± 3% of the actual value? Use a 95% confidence level. (5 points)

 

 

2. How large a sample should be taken if the error is increased to ± 6%? (5 points)

1. In 1994 in Great Britain there was hot debate over a regulation that required bigger beer glasses to accommodate a full 20-ounce British pint and a creamy head. Brewers and pub landlords would be fined for selling less. As a test, an agent visited a pub at nine random times, ordering a draft on each visit and found that the sample mean was 19.9389 ounces with a sample standard deviation of .1498 ounces. Would you conclude that on average this pub was serving glasses of beer with less than 20 ounces? (Test at the 5% level.) (15 points)

 

 

 

 

 

 

 

2. According to the long-since expired bottle in my desk drawer, there are 4 milligrams of Chlorpheniramine Maleate in each of my allergy tablets. I’m not a Pharmacist, but I am willing to assume that it is unacceptable for each of these tablets to have significantly more or less than 4 mg of this ingredient. You are hired to test the production facility for accurate measurement of ingredients in these tablets. How would you design, execute, and interpret your hypothesis test? Discuss the steps you would take to minimize and the ramifications of making both Type I and II error in this case. Be as specific and as thorough as possible. (25 points)

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