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Please print your name here: / Bus. 500Fall 2010
Todd Easton
Midterm Exam
Before beginning the exam, please read the following pledge and sign it:
I promise that I will not send or receive email, or surf the Web, during this exam. I promise that I won’t look at other students’ monitors or exam answers. I promise that the only outside material I will rely upon is my 3 x 5” card.______
Please:
a)Answer questions 1) through 3) on this copy of the exam. Answer questions 4) & 5) on this exam or using Excel—one or the other.
b)Show all your work (if you use Excel, type or copy each formula).
c)Present each numerical answer you calculate with a complete sentence (as I asked you to do for the homework).
d)Write each requested explanation with a complete sentence.
e)Do not use PHStat
f)If a question is about a sampling situation, assume the population size is very large, compared to the sample.
g)When you print, print all your sheets at the same time and let me bring them to you. Before you print, please check Print Preview to be sure you are printing what you intend. Put your name in the top-right corner of each sheet you print.
1) [4 pts.] The bar chart at right describes the distribution of values taken on by a variable. One bar in the chart is surrounded by an oval. Briefly explain the information conveyed by that bar./
2) [14 points] The director of an employment agency wishes to study various characteristics of its job applicants. A sample of 150 applicants is selected and the following information about education and current job duration is collected:
College Graduate?Held job 5 years or more? / Yes / No / Total
Yes / 25 / 45 / 70
No / 55 / 25 / 80
Total / 80 / 70 / 150
a) What is the probability that an applicant is a college graduate and has been on the job five years or more?
Show work for a) here.b) Given that the applicant is a college graduate, what is the probability that he or she has held their current job five years or more?
Show work for b) here.c) Explain the difference between question a) and question b).
3) [12 pts.] To the right you can see two graphs. Both refer to the diameters of the ping-pong balls produced in a factory during a day. The shaded area in one shows the likelihood the diameter of a ball, selected at random, will be 1.28” or less. The shaded area in the other shows the likelihood the sample meandiameter of a random sample of 16will be 1.28” or less.a) Put an “X” in the box above the statement that correctly identifies the graphs:
The top graph shows mean diameters for the sample, while the bottom graph shows individual ball diameters. / The top graph showsindividual ball diameters, while the bottom graph shows mean diameters for the sample.
b) Provide a complete explanation of why the shaded area is much larger in the top graph than in the bottom one. /
4) [18 pts.] A manufacturer of aspirin claims that the chance a headache sufferer will get relief with just two of their aspirin is 54%.
a) Suppose the claim is true. How could it happen that 50% of a random sample of 50 headache sufferers gets relief? Assume there are no errors in the sampling and in the analysis of the sample.
b) Suppose the claim is true. What is the probability that, in a random sample of 50 headache sufferers, 50% or fewer get relief?
Note: There are two different ways to do this problem with the techniques we’ve learned. Either approach is fine.
Show work here.5) [20 pts.] Suppose you are responsible for product quality at a paper plant. You take random samples of output during each two-hour period. For one particular two-hour period, the sample mean thickness was 4.015 thousandths of an inch for the 16 sheets you sampled. The sample standard deviation was .00675 thousandths of an inch.
Note:It works fine to do this problem in “thousandths of an inch”. That is, you don’t need to write .00000675 inches.
a) Calculate a 95% confidence interval for the population mean paper thickness./ Show work here.
b) Would you need to make any assumptions to calculate this interval? Please briefly explain.