This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 11/15/11 Thinking Challenges Chapter 10 Thinking Challenge Which of the following research situa:ons is most likely to use an independent-measures design? a) Evaluate the effec:veness of a training program by measuring how much faster workers complete a task with four weeks of training. b) Evaluate the effec:veness of a flu vaccine by measuring an:body levels before and aGer the vaccine administra:on. c) Evaluate the difference in verbal skills between male and female students. d) Evaluate the development of verbal skills between first and fourth year of college for a sample of female students. Pooled Variance t-Test Thinking Challenge You're a research analyst for General Motors. Assuming equal variances, is there a difference in the average miles per gallon (mpg) of two car models ( = .05)? You collect the following data: Sedan Van Number 15 11 Mean mpg 22.00 20.27 Std Dev 4.77 3.64 How much difference would you expect? 1 11/15/11 Pooled Variance t-Test Solu:on H0: 1 - 2 = 0 (1 = 2) H1: 1 - 2 0 (1 2) = .05 df = 15 + 11 - 2 = 24 Cri:cal Value(s): Test Statistic: Decision: Do not reject at = .05 Conclusion: There is no evidence of a difference in means. Test Sta:s:c Calcula:ons How Much Difference Would You Expect? We are 95% certain that the interval from 1.82 to 5.28 includes the difference in average miles per gallon for the populaCon of all GM sedans and vans. 2 11/15/11 Thinking Challenge In what type of test is the variable of interest the difference between the values of the individual observa:ons themselves? a) A test for the equality of variances from two independent popula:ons b) A test for the difference between the means of two related popula:ons c) A test for the difference between the means of two independent popula:ons d) All of the above Paired t-Test: Thinking Challenge Assume you work in the finance department. Is the new financial soGware package faster ( = 0.05 level)? You collect the following data entry :mes: User Current SoGware (1) New SoGware (2) Difference Di C.B. 9.98 Seconds 9.88 Seconds .10 T.F. 9.88 9.86 .02 M.H. 9.84 9.75 .09 R.K. 9.99 9.80 .19 M.O. 9.94 9.87 .07 D.S. 9.84 9.84 .00 S.S. 9.86 9.87 - .01 C.T. 10.12 9.86 .26 K.T. 9.90 9.83 .07 S.Z. 9.91 9.86 .05 d= d
n i =.084 Paired t-Test: Solu:on Is the new financial soGware package faster ( = 0.05 level)? H0: d 0 H1: d > 0 _ d= Reject =.05 .084 =.05 df = n - 1 = 9 Cri:cal Value=1.8331 Test Sta:s:c: 1.8331
Decision: Reject H0 t Stat. in the rejec:on region Conclusion: The new soGware package is faster. 3 11/15/11 Thinking Challenge A compe:tor of the cell phone your store carries (CellTalk) claims that a lower percent of their phones are defec:ve than the percent defec:ve claimed by the CellTalk salesperson. You check a sample of each manufacturer's product. Can we support the compe:tor's claim, using =. 05? How much difference can we expect? Cell phone sample informa:on: Product Number Defec:ve Number Checked CellTalk p1 15 150 Compe:tor's brand p2 6 150 Thinking Challenge z test of H0: 1 - 2 0 versus Ha: 1 - 2 > 0: Zcrit = 1.645 Reject H0: Support compe:tor's claim; a significantly lower propor:on of their phones are defec:ve. We are 95% certain that between .3% and 11.7% is the difference in the popula:on propor:on defec:ve of all the compe:tor's cell phones vs. CellTalk. F-Test for Two Variances Thinking Challenge You're an analyst for the Power & Light Company. At the = .05 level, is there evidence of a difference in variances between the electricity consump:on of single-family homes in 2 towns? Town 1 Town 2 Number 25 21 Mean $ 85 $ 68 Std Dev $ 30 $ 18 4 11/15/11 F-Test for Two Variances-- Solu:on H0: 12 = 22 H1: 12 22 = .05 df1 = 24 df2 = 20 Cri:cal Value(s): Reject
.025 0 2.41 F Test Statistic: Decision: Reject H : at = .05 0 Conclusion:
There is evidence of a difference in variances --town 1 is more variable. Chapter 11 Thinking Challenge For an experiment comparing more than two treatment condi:ons you should use analysis of variance rather than separate t-tests because a) You are less likely to make a mistake in the computa:ons of ANOVA b) A test based on variances is more sensi:ve than a test based on means c) ANOVA has less risk of a Type I error d) ANOVA has less risk of a Type II error 5 11/15/11 M1 M2 M3 10 11 13 9 16 8 5 9 9
SS 14 26 14 26 Grand mean = 13 One-Way ANOVA Thinking Challenge M4 18 23 25 8 12 10 22 SSA = How do means of each sample differ from grand mean? SSW = How do individual values differ from sample mean? SST = SSA + SSW ANOVA Summary Table Solu:on One-Way ANOVA Solu:on H0: 1 = 2 = 3 = 4 H1: Not all popula:on means are equal = .05 df1 = 3 df2 = 8 Cri:cal Value(s): Test Statistic: Decision: Reject H0 at = .05 Conclusion: There is evidence pop. means are different. 6 11/15/11 The Tukey-Kramer Procedure: Example Compute Cri:cal Range: (con,nued) Compare: Three of the absolute mean differences are greater than the cri:cal range. Therefore, method 4 has a significantly longer learning :me but there is no significant difference among the other methods at a 5% level of significance. Thinking Challenge A consumer preference study compares the effects of three different boule designs (A, B, and C) on sales of a popular fabric soGener using a completely randomized design. The number of boules sold in 24 hours is recorded at 15 supermarkets, each randomly assigned to carry one design. Here is the Excel output: Write the hypotheses, decision, and conclusion. Carry out the Tukey-Kramer follow-up test. Which boule design is best? Thinking Challenge Write the hypotheses, decision, and conclusion. H0:A=B=C Ha:Not all popula:on means are equal. Reject H0. At least one pop. mean is different from another. Tukey-Kramer: Sample Means: A = 16.6 n = 5 B = 32.8 n = 5 C = 24.8 n = 5 So design B is best. 7 11/15/11 Thinking Challenge A two-factor experiment means that the experimental design includes a) Two independent variables b) Two dependent variables c) An interac:on between the independent and dependent variable d) Exactly two separate groups of subjects Is there a difference in age of workers at three company plants? Is there a difference in age of workers at three company plants? Hypotheses: H0:Plant 1=Plant 2=Plant 3 Ha:Not all popula:on means are equal. Decision: Reject H0. Conclusion: At least one popula:on mean is different from another. 8 11/15/11 The Tukey-Kramer Procedure: Follow Up Compute Cri:cal Range: Compare: All of the absolute mean differences are greater than cri:cal range. Therefore there is a significant difference between each pair of means at 5% level of significance. The average age of all workers at Plant 2 is highest; average age at Plant 3 is lowest. 9 ...
View Full Document
This note was uploaded on 02/07/2012 for the course GEN BUS 303 taught by Professor Mullins during the Spring '08 term at Wisconsin.
- Spring '08