week 3 homework on HT and ANOVA

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School

Saint Joseph's University *

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MISC

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Statistics

Date

Feb 20, 2024

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docx

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6

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1 Name:___Michael Angiolillo___________________________________________________ Please analyze the following problems in JMP and answer the questions below. Copy/Paste JMP screen shots of your output in each section. 1. It is well-known that the wait times for rides at a local amusement park are much longer on the weekends than weekdays. Historically, the wait time for popular rides on weekends average to be 10.5 minutes. After recent discussions you have had with friends who visited this amusement park, you heard complaints on how long they waited in line for rides. You decide to test the hypothesis that wait times are longer than 10.5 minutes on average. Over the course of a few weekends, you record the wait time for 22 visitors in line for rides. The data is below (in minutes). Is there enough evidence in the collected data to support your hypothesis that the average amusement park ride wait time exceeds 10.5 minutes? You opt to conduct the test at a α = 5% level of significance. Ride wait times: 21.6, 10.4, 9.1, 16.2, 17.8, 13.0, 9.8, 10.5, 10.2, 10.3, 11.0, 14.1, 12.0, 10.4, 9.3, 10.5, 16.0, 7.5, 16.7, 8.2, 9.0, 10.3 a) Check the assumptions about the shape of the data. State what you have found and the specific output used to support it. After using the Goodness of Fit test, I see that the p-value is .0067 which means we reject the null since it is lower than the alpha .01 for GoF. Therefore, the data is skewed. With the data not being approx. normal, we must use medians for a measure of center and not mean. b) State the null and alternative hypothesis about the claim of amusement park ride wait times. Ho: median <= 10.5 mins of wait time Ha: median > 10.5 mins of wait time c) What is the p-value for the hypothesis test in part (b)? p-value is .0321
2 d) What is your conclusion about ride wait times at this amusement park? Write your answer in a sentence or two. With a p-value of .0321 and an alpha value of .05, we reject the null. This means there is statistically significant evidence to say that the median wait time for rides at this amusement park is greater than 10.5 minutes. 2. A well-known conglomerate claims that its detergent “whitens and brightens better than all the rest.” In order to compare the cleansing action of the top three brands of laundry detergents, 24 swatches of white cloth were soiled with red wine and grass stains and then washed in front- loading machines with the respective detergents. The following whiteness readings were obtained: Detergent A Detergent B Detergent C 84 78 87 79 74 75 87 81 82 85 86 77 84 86 78 89 89 79 89 75 77 83 79 78 a. Check the necessary assumptions needed to do a one-way ANOVA model. Show the JMP output for each assumption and write a sentence about what the output indicates. All p-values for the GoF test are above .01, meaning we can proceed with ANOVA because they aren’t skewed. A: .9780 B: .8177 C: .0202. Also, the O Brien p-value is .5632 so we reject the null, meaning the variance is roughly equal and we can proceed. SCREENSHOTS ARE BELOW b. Specify the null and alternative hypotheses to test whether there are some differences in the average whitening effectiveness of the three detergents Ho: meanA = meanB = meanC Ha: at least one difference between the 3
3 c. At the 5% level of significance, what is the conclusion to the analysis? Your answer should be thorough and several sentences long. Show screen shots of the JMP output you used to draw these conclusions. The ANOVA p-value is .0741. This is not less than the alpha value of .05. Therefore, we fail to reject the null. There is not statistically significant evidence to state that there is any difference between detergents A, B, or C.
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