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Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin Biostats SDS 328M Homework 5 Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name and your lab time. Show all work for full credit. Round all answers to at least 3 decimal places and assume, unless otherwise noted, that α=0.05 1. To determine how talking on a cell phone affects driving ability, a researcher set up an experiment where she measured the reaction times (in milliseconds) of a sample of 12 adults under two conditions. Each participant was measured in a driving simulator while talking on a cell phone and then again without distraction. The order was randomized, and the results are displayed below: Reaction Time (ms) Participant No. 1 2 3 4 5 6 7 8 9 10 11 12 No distraction 604 556 513 556 531 537 467 525 470 515 499 589 Talking on cell 636 623 542 543 580 559 554 626 468 525 457 679 a. You want to use this data to test if cell phone use increases reaction time, on average. Create a boxplot to confirm the relevant assumption for this analysis. (4pt) b. Does this data pass all of the relevant assumptions (if it was a random sample with independent observations)? (1pt) c. Run a hypothesis test to answer your research question. Show all of your work and include all steps for full credit. (4pt) d. List at least one possible confounding variable in this study. (1pt) 2. An industrial plant dumps its waste into a nearby river, but claims that it is not impacting the native fish that live in the river. You’ve measure the calcium concentration from a random sample of 18 locations in the river and calculated a mean of 97.4 mg/L, with a standard deviation of 4.1 mg/L. The fish are able to tolerate calcium concentrations up to 95 mg/L. a. Assuming a normal distribution, calculate a 95% confidence interval for the mean calcium concentration in the river. (3pts) b. Does your data suggest that the fish are being negatively impacted? Explain your answer. (2pt) c. Assuming that you held everything else constant, how would the width of the confidence interval change if you doubled your sample size from 18 to 36? Would it become wider, narrower, or stay the same? (1pt)
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Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin 3. A study was conducted to compare the resting pulse rate among smokers and non-smokers. The data are summarized in the table below. The pulse rate distribution in each group can be assumed to be normal, and equal population variances can be assumed in the two groups. Resting pulse rate (bpm) Group Sample size Mean Smokers 35 82.1 Non-smokers 40 73.7 Conduct the appropriate test to see if the mean resting pulse rate for smokers and non-smokers is the same or not. Show all of your work and include all steps for full credit. (4pt) Given: °± ² ̅ 1 −² ̅ 2 = 4.5
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