Day 6 DAILY on Paired T

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Rochester Institute of Technology *

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146

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Statistics

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Apr 3, 2024

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Class Day/Time: Name: Type your Name STAT 146 Daily 6 Comparing two means – paired data Problem 1: We are interested in studying the effect that exercise has on the level of Lactic acid in the blood. Fifteen people had their blood lactate levels measured before and after playing three games of racquetball. The data are in the file LacticAcid.MTX. As a researcher, you believe that the lactic acid levels increase after exercise. A. Explain why we would consider this paired data, as opposed to independent data. B. Perform the appropriate hypothesis test to determine if the lactic acid levels are statistically higher after exercise. Use alpha = 0.05. Show the complete testing process. Problem 2: An insurance company is concerned that garage A is charging too much for repairing damage to cars. The same ten damaged cars were taken to both garage A and garage B for estimates. The Garage Data.mtw file in MyCourses has the estimates for repairing the cars (in dollars). A. Are we studying two samples of paired data or two samples of independent data? Explain. B. Build and interpret a 95% confidence interval for the mean of the differences in car repair estimates for garages A and B. Be sure to include your Minitab output. Write a follow-up sentence, indicating if the CI shows a statistical difference and if one garage has a statistically higher estimate. STAT 146 Intro to Stat 2 Daily 6 Page 1 of 3

Problem 3: Ecologists have developed different methods for estimating the number of seeds in soil samples. The data set SeedCount.MTX provides the seed counts when using both the direct and stratified methods on each of 27 soil samples (specimens). You will NOT need the data set. I have already produced the Minitab output. Using the confidence interval built on the mean of the differences in seed counts, please provide a statistical interpretation. Then, write a follow-up sentences that clearly indicates if the methods are statistically different. If they are different, then indicate which method counts more seeds. Problem 4: Read through each research situation and decide if we are studying two independent means (2- Sample T) or paired means (Paired t). Explain your decision. YOU ARE NOT COMPLETING ANY TEST, just deciding WHICH TEST you would use based on the type of samples that were taken. A. Researchers conducted a study in which two groups of students were asked to answer 42 Trivial Pursuit questions. Before answering the questions, students in group 1 were asked to spend 5 minutes thinking about and picturing themselves as a professor. Students in group 2 were asked to spend 5 minutes thinking about rowdy football fans. Which test would be used to determine if there is a difference in the mean number of Trivial Pursuit questions that each group can answer? B. In an experiment, participants are asked to react to a stimulus, i.e., pressing a certain keyboard key when they see a certain color on the computer screen. First, participants were asked to press a key when seeing a blue screen. Each participant’s reaction times (in seconds) are measured. The same person is then asked to press a key when seeing a red screen. Each participant’s reaction times (in seconds) are measured a second time. Which test would be used to determine if the reaction time to the blue stimulus is greater than that of the red stimulus? STAT 146 Intro to Stat 2 Daily 6 Page 2 of 3

C. A clinic provides a program to help their clients lose weight and asks a consumer agency to investigate the effectiveness of the program. The agency takes a sample of 15 people, weighing each person in the sample before the program begins and 3 months later to produce the data. Which test should be used to determine whether the program is effective? STAT 146 Intro to Stat 2 Daily 6 Page 3 of 3

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