HS312 Unit 8 Assignments Unit 7 & 8, Exercises

Unit 7, Topic 27, Exercise 27­20 Muscle Fatigue Do women or men experience fatigue more quickly while exercising? To investigate this issue, researchers recruited healthy young adults to participate in a study (Hunter et al., 2004). The researchers first measured the strength of each person by the torque exerted at the wrist during amaximal voluntary contraction. Then they matched up each of the comparable strength (within men in the study with a woman ofof the maximal torque exerted). Next, they asked each subject tocomplete a prescribed series of exercises with their elbow flexor muscles and elbow extensor musclesuntil they lacked the strength to continue. Researchers recorded how long it took before failure at thisexercise task for each subject. a. Calculate the correlation coefficient between time until muscle fatigue for men and time until musclefatigue for women. Round your answer to three decimal places. b. Comment on what this correlation coefficient suggests about whether men and women of similarstrength tend to have similar times until muscle fatigue. The correlation coefficient suggests there is a strong, negative associationbetween fatigue times. the absolute tolerance is +/­0.001 Unit 7, Topic 28, Exercise 28­32 The Kentucky Derby is the most famous horse race in the world, held annually on the first Saturday inMay at Churchill Downs race track in Louisville, Kentucky. This race has been called “The Most Exciting Two Minutes in Sports” because that’s about how long it takes for a horse to run its Consider the winning time (in seconds) for every year since 1896. a. For predicting winning time from year, the least squares line has intercept coefficient and slope coefficientmile track. seconds seconds per year. Use this information to report the equation of the least squares line, using good statistical notation. Use “year” for the name of the predictor variable. b. Based on the following residual plot, comment on whether a straight line appears to be a reasonablemodel for the relationship between winning time and year. Unit 7, Topic 29, Exercise 29­09 Draft Lottery The United States Selective Service conducted a lottery to decide which young men would be drafted intothe armed forces (Fienberg, 1971). Each of thebirthdays of the year was assigned a draft number. Young men born on days assigned low draft numbers were drafted. The correlation coefficient betweendraft number and sequential birthday for the 1970 lottery was a. Determine the probability that a fair random lottery would produce a correlation coefficient so far fromzero, simply by random chance. In other words, determine the value for testing whether thepopulation correlation coefficient equals zero, against a two­sided alternative. Report the test statistic aswell as the value. [Hint: There were numbers in this draft.] Round the test statistic to two decimal places. Use thedistribution table to find a range for the value. If there is no lower limit on thefor the lower limit. If there is no upper limit on the for the upper limit. The test statistic isvalue Unit 7, Topic 27, Exercise 27­20 The correlation coefficient between draft number and sequential birthday for the 1971 lottery was. b. Repeat part a for the 1971 lottery. Round your answer for the test statistic to two decimal places. Use therange for thevalue. If there is no lower limit on the no upper limit on the distribution table to find afor the lower limit. If there isfor the upper limit. The test statistic isvalue c. Summarize what thesevalues reveal about the fairness of these two lotteries.

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