Stats for Strategy HOMEWORK 3 (Topics 4 and 5) (revised spring 2015) DIRECTIONS Data files are available from the main Stats website for many exercises. (Smaller data sets for other exercises can be typed directly into MINITAB.) Use your own paper to write out and label the Four Steps of Hypothesis Testing. Use 5% significance whenever the textbook doesn t specify the level. Text exercises marked with the icon are accessed from the Supplementary Exercises (SE) file posted on the Stats website, not the textbook itself. See How To Succeed With Stats Homework on Notebook page 7! This is a great way to s-q-u-e-e-z-e as much knowledge and understanding as possible from the Homework for great quiz and exam preparation! A. Opening Data Files in Virtual Desktop. Using MINITAB for Chi-Square Tests To open a data set from the Stats website you must trick Virtual Desktop into opening the file from the university computer on which MINITAB is actually running! Do this by going through using Virtual Desktop s web browser, just as if you had opened a browser from a workstation in the Discussion computer lab. 1. Log on to Virtual Desktop: http://virtualdesktop.uiowa.edu 2. Open the data file Topic 4 Example 1 from the Stats website. Use the steps below from within Virtual Desktop: Web Browsers > Firefox > Navigate to course website (it may be easiest to google Blake Whitten ) > Go to MINITAB Data Sets link, click the file to open Did you successfully open the file? (continued next page) 1
3. Now let s use MINITAB to get the three-in-one (observed, expected, contributions) χ 2 table shown for Topic 4 Example 1 on about page 92 in the Notebook. Open the Notes to about page 92. Do you see the MINITAB table? Use these MINITAB steps on your open Topic 4 Example 1 data file: Stat > Tables > Chi-Square Test for Association > (Choose Summarized data in a two-way table) > (Select columns Women, Men) > OK Your table probably shows two numbers in each cell instead of three (it s missing the contributions) so let s request all three from MINITAB. Re-run MINITAB and add these steps: Statistics > (Check box Each cell s contribution to chi-square) Now your table and the Notebook s table should match! Note: The correct χ 2 statistic is Pearson Chi-Square = 135.592. Simply ignore the line below. (We won t use Likelihood Ratio Chi-Square = 142.207. ) 4. Answer the following questions: (a) Find MINITAB s exact χ 2 statistic. (b) Find MINITAB s P -value. (c) Complete the Decision in Step 3: Is H 0 rejected? Why or why not? 2
B. Chi-Square Tests (Chapter 9) Exercise 9.36 (p. 518) Ignore the book s directions for this exercise. Follow these directions instead: (a) Calculate the degrees of freedom for the data table. (b) Look up the critical value for the χ 2 test at 5% significance. (c) Perform the χ 2 test in Four Steps. Refer to Topic 4 Example 2 in the Notes to recall how to do this. (Calculate χ 2 by hand in Step 2.) (d) Enter the data table into a MINITAB worksheet and perform the χ 2 test in MINITAB. What are MINITAB s exact χ 2 value and P -value? (e) Redo Step 3 of the Four Steps, using the P -value instead of critical value for your decision. (f) Use the 2 Proportions procedure in MINITAB to find and interpret a 95% CI for percent of general interest ads vs. men s ads which are not sexual. (g) Does the comparison of proportions in (f) reinforce or support the conclusion from the χ 2 test? Explain why or why not. (h) Use the 2 Proportions procedure in MINITAB to find and interpret a 95% CI for percent of women s ads vs. men s ads which are sexual. (i) Does the comparison in (h) reinforce or support the conclusion from the χ 2 test? Explain why or why not. (j) Use the table of χ 2 contributions to explain why one of the above pairs of proportions reinforces the χ 2 test but the other does not. Exercise 9.44 (Calculate χ 2 by hand, and use Four Steps. Do not use MINITAB.) Exercise 9.45 (Calculate χ 2 by hand, and use Four Steps. Do not use MINITAB.) Supplementary Exercise 9.8 (SE file p. 107) Use MINITAB and Four Steps. Also add part (b): (b) Choose two proportions whose comparison reinforces or supports the conclusion from the χ 2 test. Answer questions (i) (iii) below: (i) Define the proportions. (ii) Find and interpret a 95% confidence interval. (iii) Explain how the CI supports the χ 2 test. 3
C. Comparing Two Means (Chapter 7) In each exercise determine whether the two samples are paired or independent. Ask this question: Is there a pairing mechanism? Refer to Example 1 (Asset Ratios) in the Topic 5 Notes. Open the data file CACL Ratio from the Data Sets page. Apply MINITAB to reproduce the three outputs for Example 1 shown beginning about page 104 in the Notebook. (Follow MINITAB steps shown in the Notebook.) Are you successful? Refer to Example 2 (Fuel Additive) in the Topic 5 Notes. Open the data file Fuel Additive. Then reproduce the (correct) MINITAB output shown on about page 110 in the Notebook. Exercise 7.60 (p. 423) Also interpret the answer to (a). Supplementary Exercise 7.20 (SE file p. 88)) Ignore parts (a) and (b). Do part (c) only by labeling and writing Four Steps. Save time! Open the data file Supplementary Exercise 7.20 on the MINITAB Data Sets page of the Stats website instead of typing the data by hand. Supplementary Exercise 7.21 Also interpret the confidence interval for a client. Exercise 7.10 (p. 406) Exercise 7.11 Also interpret answer. Exercise 7.45 (p. 416, use the data file) Add parts (c) and (d): (c) Find three 95% CI s for mean mpg: By computer, by driver, and for the difference. (d) True or False: With 95% confidence, the driver calculates worse gas mileage than the computer by between 1.419 and 4.041 mpg, on average. Exercise 7.47 Exercise 7.89 (p. 438, use data file) Ignore the book s directions for this exercise. Follow these directions instead: (a) Test for a difference in mean ego strength, using 1% significance. (b) Find a 99% confidence interval for the difference in mean ego strength. (c) Summarize answers (a) and (b) in plain English for a psychologist who is familiar with ego issues but not with Statistics. Exercise 7.46 (p. 417) Ignore part (b). Do parts (a), (c), (d) only. Also interpret part (d). 4
Exercise 7.85 (p. 437) Exercise 7.86 D. Additional Practice (1) The American Automobile Association (AAA) is a national organization which also has 50 state chapters. Members of the Iowa chapter of the AAA would like to compare prices of regular gasoline to prices of diesel fuel within the state of Iowa. In particular, suppose that the Iowa chapter would like to test the theory that diesel is more expensive on average than regular gasoline at Iowa service stations on Sept. 30, 2015. It s known that fuel prices tend to vary by location, due to factors such as number of competing service stations nearby and transportation costs from the nearest refinery or fuel depot. The AAA national organization has provided the Iowa chapter with a database of prices, shown in the table below. The database was developed as follows: Five zip codes were randomly selected from all zip codes in the state of Minnesota, and five zip codes were randomly selected from all zip codes in the state of Iowa. For each selected zip code, the price of diesel fuel on Sept. 30, 2015 was recorded from a service station within that zip code. Also, the price of regular gas on Sept. 30, 2015 was recorded from a service station within the same zip code. (The stations measured for these two prices in any particular zip code are not necessarily the same.) Price (dollars/gallon) Price (dollars/gallon) Zip Code City State for Regular Gas for Diesel Fuel 50005 Minerva Iowa 3.66 3.73 50021 Ankeny Iowa 3.63 3.60 55005 Bethel Minnesota 3.81 3.88 56258 Marshall Minnesota 3.86 3.92 50101 Galt Iowa 3.72 3.80 56678 Becida Minnesota 3.83 3.88 55732 Pike Minnesota 3.93 3.98 50438 Miller Iowa 3.60 3.67 52050 Greeley Iowa 3.58 3.64 55383 Norwood Minnesota 3.84 3.87 Avg. = 3.746 Avg. = 3.797 Test the theory, using 5% significance. (a) Choose the correct P -value from the following choices: (A) 0.000 (B) 0.034 (C) 0.141 (D) 0.190 (b) Decide. (c) Interpret. 5
(2) DIRECTIONS: Don t make any calculations or use MINITAB! Instead refer only to the MINITAB output on this page and the next. Market researchers think that background music might influence the mood and purchasing behavior of customers. One study in a supermarket in Northern Ireland compared three choices for the supermarket s sound system: no music, French accordion music, and Italian string music. Under each music choice, the researchers recorded the numbers of bottles of French, Italian, and other wine sold in one week. The data from the study are shown below. Music Wine None French Italian French 30 39 30 Italian 11 1 19 Other 43 35 35 (a) Compare the choice of Italian music to the choice of no music for impact upon the relative popularity of Italian wine among customers. With 95% confidence, does this comparison support or reinforce the conclusion from the χ 2 test? (Choose the single best answer.) (A) Yes (B) No (C) Impossible to determine, based on the available MINITAB output (b) Compare the choice of French music to the choice of no music for impact upon the relative popularity of French wine among customers. With 95% confidence, does this comparison support or reinforce the conclusion from the χ 2 test? (A) Yes (B) No (C) Impossible to determine, based on the available MINITAB output None French Italian All 1 30 39 30 99 34.22 30.56 34.22 0.5209 2.3337 0.5209 2 11 1 19 31 10.72 9.57 10.72 0.0075 7.6724 6.4038 3 43 35 35 113 39.06 34.88 39.06 0.3971 0.0004 0.4223 All 84 75 84 243 Pearson Chi-Square = 18.279, DF = 4, P-Value = 0.001 Likelihood Ratio Chi-Square = 21.875, DF = 4, P-Value = 0.000 6
Test and CI for Two Proportions 1 19 84 0.226190 2 11 84 0.130952 Estimate for difference: 0.0952381 95% CI for difference: (-0.0196913, 0.210168) Test for difference = 0 (vs not = 0): Z = 1.61 P-Value = 0.107 Test and CI for Two Proportions 1 19 31 0.612903 2 11 31 0.354839 Estimate for difference: 0.258065 95% CI for difference: (0.0177143, 0.498415) Test for difference = 0 (vs not = 0): Z = 2.03 P-Value = 0.042 Test and CI for Two Proportions 1 39 99 0.393939 2 30 99 0.303030 Estimate for difference: 0.0909091 95% CI for difference: (-0.0412249, 0.223043) Test for difference = 0 (vs not = 0): Z = 1.34 P-Value = 0.179 Test and CI for Two Proportions 1 39 75 0.520000 2 30 84 0.357143 Estimate for difference: 0.162857 95% CI for difference: (0.0102662, 0.315448) Test for difference = 0 (vs not = 0): Z = 2.07 P-Value = 0.039 (end of assignment) 7