Week 4 Practice Worksheet PSY/315 Version 6 1 University of Phoenix Material Week 4 Practice Worksheet Prepare a written response to the following questions. Chapters 9 &11 1. Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances. The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means. Hypothesis Test: Independent Groups (t-test, unequal variance) Prada 12.170 1.056 10 Oracle 14.875 2.208 12 16 -2.7050 0.7196 0 -3.76 .0017 -4.2304 -1.1796 1.5254 mean std. dev. n df difference (Prada - Oracle) standard error of difference hypothesized difference t p-value (two-tailed) confidence interval 95.% lower confidence interval 95.% upper margin of error 2. The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of ten customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of fourteen customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample Assuming Unequal Variances was used. At the .01 significance level is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but is Copyright ©2013 by Pearson Education, Inc. All rights reserved. Used with permission Week 4 Practice Worksheet PSY/315 Version 6 2 unfamiliar with the t test for independent means. Hypothesis Test: Independent Groups (t-test, unequal variance) Peach Street 15.8680 2.3306 10 Plum Street 18.2921 2.5527 14 mean std. dev. n 20 df difference (Peach Street Plum Street) standard error of difference hypothesized difference -2.42414 1.00431 0 -2.41 .0255 t p-value (two-tailed) confidence interval 99.% lower confidence interval 99.% upper -5.28173 0.43345 2.85759 margin of error 3. Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value? Hypothesis Test: Independent Groups (t-test, pooled variance) Larry 4.77 1.05 40 George 5.02 1.23 50 88 -0.25000 1.33102 1.15370 0.24474 0 -1.02 .3098 mean std. dev. n df difference (Larry - George) pooled variance pooled std. dev. standard error of difference hypothesized difference t p-value (two-tailed) Copyright ©2013 by Pearson Education, Inc. All rights reserved. Used with permission Week 4 Practice Worksheet PSY/315 Version 6 -0.73636 0.23636 3 confidence interval 95.% lower confidence interval 95.% upper 0.48636 margin of error Chapters 11 & 12 4. A consumer organization wants to know if there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount toy stores, five variety stores, and five department stores. The results are shown below. Discount toy Variety Department $12 15 19 13 17 17 14 14 16 12 18 20 15 17 19 An ANOVA was run and the results are shown below. At the .05 significance level, is there a difference in the mean prices between the three stores? What is the p-value? Explain why an ANOVA was used to analyze this problem. One factor ANOVA Mean n Std. Dev 13.2 5 1.30 Discount Toys 16.2 5 1.64 Variety 18.2 15.9 5 15 1.64 2.56 Department Total SS 63.33 28.40 91.73 df 2 12 14 MS 31.667 2.367 ANOVA table Source Treatment Error Total F 13.38 pvalue .0009 Copyright ©2013 by Pearson Education, Inc. All rights reserved. Used with permission Week 4 Practice Worksheet PSY/315 Version 6 4 5. A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets? Plan A Plan B Plan C 5 6 7 7 7 8 4 7 9 5 5 8 4 6 9 An ANOVA was run and the results are shown below. At the .01 significance level, is there a difference in the weight loss between the three plans? What is the p-value? What can you do to determine exactly where the difference is? One factor ANOVA Mean n Std. Dev 5.0 5 1.22 6.2 5 0.84 8.2 6.5 5 15 0.84 1.64 SS 26.13 11.60 37.73 df 2 12 14 MS 13.067 0.967 Plan A Plan B Plan C Total ANOVA table Source Treatment Error Total F 13.52 pvalue .0008 Copyright ©2013 by Pearson Education, Inc. All rights reserved. Used with permission