NAME:
Exam 2
Fall 2000
You may use additional sheets of paper to solve the following questions, but you please report your results and conclusions in the space provided. Whenever possible, show your work for potential partial credit. NOTE: When performing numerical calculations, keep at least 4 digits after a decimal. (I.e., do NOT round .2265 to .23 or .227) BUDGET YOUR TIME WISELY!
1. The price of
gasoline in the U.S. is considered a random variable x. What is the difference
between the probability distribution of x and the probability distribution of 
, the sampling
distribution? Explain. (8 points)
2. Suppose the average undergraduate college student drinks 6 alcoholic beverages in a typical week. The population standard deviation is 3.5 drinks per week and a sample of 212 college students will be selected.
a. Show the sampling distribution of the sample mean number of weekly drinks based on the sample of 212. (3 points)
b. What is the probability that the sample mean for the 212 students will be within ± .5 drinks of the population mean? (5 points)
2. What important role does the Central Limit Theorem serve whenever a point estimator is used to estimate a population parameter? (10 points)
3. In his book Privacy for Sale, Jeffrey Rothfeder explains the story of Safeway Stores’ installation of dashboard computers on 782 trucks. The computer gave a report showing any abnormal condition. For example, if a truck’s engine idled for 25 minutes on a trip for which the average idling time was only 10 minutes, the driver would be questioned and possibly suspended.
Assume that a Canadian plant manager wished to determine an estimate of a mean idle time for the trucks. Idle times from a random sample of size 51 were recorded. The sample mean was 11.5 minutes, and the sample standard deviation was 5.3 minutes. Find a 90% confidence interval on the mean idle time for trucks. How do you interpret this interval?[1] How many idle times would you have to sample to cut the margin of error (for another 90% confidence interval) in half? (14 points)
4. Your absent-minded professor reports that survey results of college student television viewing habits have provided a standard error of the mean of .6193. The population standard deviation is 8.9533.
a. How large was the sample used in this survey? (3 points)
b. What is the probability that the estimated sample mean would be within 1.5 hours of the population mean? (5 points)
5. What is the effect of a larger sample size on the interval estimate of a population mean? Use the above problem to explain. (5 points)
6. A random sample of 50 young adult
men (20-30 years old) was sampled. Each
person was asked how many minutes of sports they watch on television
daily. The sample mean was found to be
64 minutes. Suppose that the population
standard deviation is 20 minutes. Test
to determine at the 1% significance level whether there is enough statistical
evidence to infer that the mean amount of television watched by all young adult
men is greater than 60 minutes. First
identify the null and alternative hypotheses, illustrate the rejection
range(s), test the hypothesis and interpret the result as if the reader had no
idea what you were doing. (12 points)
7. A test preparation service assures engineering students that the mean percentage of engineering students who pass their qualifying exam is greater than 77%. Assume that the scores are normally distributed. A random sample of 25 engineers indicates that 16 have passed the exam. Do these data support the claim? Use an appropriate level of significance to conduct your test. Explain your results. Would they change with a different level of significance? (10 points)
8. 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 significantly less than 4 mg of this ingredient. You are hired to test the production facility for accurate measurement of ingredients in these tablets. In the following questions, be as specific and as thorough as possible.
a. Discuss the ramifications of making both Type I and Type II errors in this case. (8 points)
b. Choose a level of confidence for your hypothesis test. Why did you choose this a? (5 points)
c. How would you design, execute, and interpret your hypothesis test? Explain every step in your methodology. (12 points)