STAT 301 – BUSINESS STATISTICS
FALL SEMESTER 2010
“Knowledge Festival” #2 – Part 1 (Computational)
This “knowledge festival” is intended to assess your mastery of the computational aspects of this course. This test is open-book, open-notes. That is, you may use any written resource material during the examination (textbook, other reference books, course notes, lecture review assignments, tables, etc.). You may not use internet-based sources, and may not confer with others. You may, of course, use a calculator. You must show your work on all problems.
There are 100 points worth of problems on this exam; relative problem weights are given in brackets. Unless the problem specifically indicates otherwise, use the traditional confidence level of 95% and the traditional significance level of

=0.05.
This “knowledge festival” is given under provisions of the Honor System of Stetson University.
The word “pledged” written before your name at the top of this page is a symbol of your ongoing commitment to the Honor System.
Enjoy!!
Question 0 [4 points; 2 each part]: a) Spell your name (correctly and legibly) at the top of the page. b) How many hours of sleep have you gotten, in the past 24 hours? __________
Question 1 [16 points; 8 each part]:
Dr. Jack File, professor of Applied Numerology at Mad Hatter Vocational-Technical
Institute, asks a random sample of five students, “How many hours of sleep have you gotten, in the past 24 hours?” a) The five members of his sample reported 8, 9, 6, 4, and 3 hours of sleep, respectively. Find the standard deviation for these data. Show your work!!! b) Give a 95% confidence interval for the mean number of hours of sleep, for all students on campus.

Question 2 [24 points, divided as indicated]:
Alphonso Ferrabosco II wonders whether people can tell coffee from used motor oil, in a blind taste test. He sets up a triangle taste test in front of the CUB. Passers-by are given three unmarked glasses (either two coffee and one used motor oil, or vice-versa), and asked to identify which one is different from the other two. a) [6] State Alphonso’s null and alternative hypotheses, in words and in symbols. b) [10] Alphonso has two hundred people participate in his study; eighty of them are able to identify correctly the “different” glass. Compute Alphonso’s test statistic. Indicate clearly whether this is a z-test or a t-test (and, if it is a t-test, how many degrees of freedom). Give the p-value for the test. c) [8] Based upon your calculations in Part B, what conclusion should Alphonso draw? State this both in statistics jargon (reject/don’t reject) and in the language of the problem.

Question 3 [18 points; 6 each part]:
Automated machinery is used to fill boxes of Chocolate Frosted Sugar Bombs breakfast cereal. The amount of cereal per box is normally distributed, with a mean of 16.2 ounces and a standard deviation of 0.4 ounces. a) What percentage of the boxes contain at least 16 ounces of cereal? b) How much cereal is in the lightest 10% of the boxes? c) What percentage of the boxes contain less than 20 ounces of cereal?
Question 4 [6 points]:
Gracetta Squornshellous is conducting a hypothesis test. She knows that she wants to use
Student’s t distribution, with 21 degrees of freedom. She has computed a test statistic of 2.42.
What is the p-value of her test? Should she reject or not reject her null hypothesis?

Question 5 [24 points, divided as indicated]:
The Sirius Cybernetics Corporation is conducting a market research study to identify whether its new product line of inflatable bowling balls sells better when packaged in a garish neon yellow box, or in a discreet beige box. They identify twelve stores to use in a test marketing campaign. Each of the twelve stores is of approximately equal size, with approximately equal levels of sales of traditional (i.e., non-inflatable) bowling balls. Stores were randomly assigned to one of two groups – a “neon yellow box” group and a “beige box” group.
Data were collected on total number of inflatable bowling balls sold at each store.
The data are given below. Also given are differences between the two sets of numbers, as well as summary statistics (mean and standard deviation) for each group of numbers. You won’t need all this information – but some of the numbers will make your computational task simpler.
Neon yellow: 14 21 13 12 31 23 mean = 19 stdev = 7.40
Beige: 18 20 24 32 27 17 mean = 23 stdev = 5.80
Difference: -4 1 -11 -20 4 6 mean = -4 stdev = 9.40 a) [6] State the appropriate null and alternative hypothesis, both in words and in symbols. b) [10] Compute an appropriate test statistic. Indicate clearly whether this is a z-test or a t-test
(and, if it is a t-test, how many degrees of freedom). Give the p-value for the test. c) [8] Based upon your calculations in Part B, what conclusion should be drawn? State this both in statistics jargon (reject/don’t reject) and in the language of the problem.

Question 6 [12 points]:
One of the questions on the first “knowledge festival” involved an American roulette wheel, which has 38 numbers (1 through 36 plus 0 and 00). The “knowledge festival” question focused on the one of the many ways you can gamble at roulette, which is to bet on a block of five numbers (namely: 0, 00, 1, 2, 3). If you place this bet and win (that is, one of those five numbers comes up), you win $6 net for every dollar bet. (You get your $1 back plus $6 more.)
Otherwise, you lose your bet.
For this wager, $1 bet has an expected net return of –3/38 (that is, you lose three thirtyeighths of a dollar, on average, for each dollar you bet) and a variance of 5.6.
If you place 500 such bets, what is the probability that you make money?