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UPX Material Title ABC/123 Version X 1 Week 4 Practice Worksheet PSY/315 Version 8 4 University of Phoenix Material Week 4 Practice Worksheet Provide a response to the following prompts. Note: Each team member should compute the following questions and submit them to the Learning Team forum. The team should then discuss each team member’s answers to ascertain the correct answer for each question. Once your team has answered all the questions, submit a finalized team worksheet. 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 as follows: 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 as follows: 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. Hypothesis Test: Independent Groups (t test, unequal variance) Prada Oracle 12.170 14.875 mean 1.056 2.208 std. dev. 10 12 n 16 df -2.7050 difference (Prada - Oracle) 0.7196 standard error of difference 0 hypothesized difference -3.76 t .0017 p-value (two-tailed) -4.2304 confidence interval 95% lower -1.1796 confidence interval 95% upper 1.5254 margin of error The previous table shows the results of this independent t test. At the .05 significance level, can you 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 who is unfamiliar with the t test for independent means. · Critical T- Value Graph · Yes, there is a difference in the mean times between both Prada and Oracle. See with a single sample it is not possible for it be compared to groups of multiple. Therefore, the choice to use an independent sample is a better option when it comes to the two groups provided above as we can use the independent sample with unequal variances. · See Excel Worksheet for the Two-Sample · According to the information provided in the excel sheet, the null hypothesis is not rejected due to the t-value being less than the critical value. 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 10 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 14 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. Hypothesis Test: Independent Groups (t test, unequal variance) Peach Street Plum Street 15.8680 18.2921 mean 2.3306 2.5527 std. dev. 10 14 n 20 df -2.42414 difference (Peach Street - Plum Street) 1.00431 standard error of difference 0 hypothesized difference -2.41 t .0255 p-value (two-tailed) -5.28173 confidence interval 99.% lower 0.43345 confidence interval 99.% upper 2.85759 margin of error 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 who is unfamiliar with the t test for independent means. · Critical T-Value Graph · Like the first problem, yes there is a difference in the means, however, these are the same stores but at different locations, so one could use a single sample for the results. However, one could use a t test for the independent means to determine if the statistical evidence is significantly different. · See Excel for Two Sample · The t stat does not fall into the critical category, so I’d say that we reject the null hypothesis on this problem. See graph linked above for Critical T-value. 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. Hypothesis Test: Independent Groups (t test, pooled variance) Larry George 4.77 5.02 mean 1.05 1.23 std. dev. 40 50 n 88 df -0.25000 difference (Larry - George) 1.33102 pooled variance 1.15370 pooled std. dev. 0.24474 standard error of difference 0 hypothesized difference -1.02 t .3098 p-value (two-tailed) -0.73636 confidence interval 95.% lower 0.23636 confidence interval 95.% upper 0.48636 margin of error 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? · Critical T-Value Graph · Yes, there is a difference between the number of calls per day between the employees, even if it is a small amount. · The p-value is .3098 · The t score is greater than the critical value, therefore it is going to reject the null hypothesis for this problem. 4. An organizational psychologist measures levels of job satisfaction in a sample of 30 participants. To measure the variance of job satisfaction, it is calculated that the SS = 120 for this sample. a. What are the degrees of freedom for the variance? · df = N – 1 · df = 30 – 1 b. Compute the variance and standard deviation (you will have to do this one by hand). · Variance = SS/n-1 · Variance = 120/29 · Variance = 4.14 · Standard Deviation = Square root of the Variance = 2.0342 Copyright © XXXX by University of Phoenix. All rights reserved. Copyright ©2013 by Pearson Education, Inc. All rights reserved. Used with permission.