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311_practice_problems - I often play Scrabble against a...

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I often play Scrabble against a friend of mine, Nicole. We want to know whether we tend to be, on average evenly matched. That is, we want to know whether our scores tend to be the same or not. I randomly pick ten games that we have played, and record our scores: Game: 1 2 3 4 5 6 7 8 9 10 McLean 272 324 316 283 357 264 310 267 330 315 Nicole 241 236 311 305 251 303 301 268 351 267 Difference 31 88 5 -22 106 -39 9 -1 -21 48 The mean for my scores is 303.8, and the standard deviation is 30.95. The mean for Nicole’s scores is 283.4, and the standard deviation is 36.66. The mean for the difference is 20.4, and the standard deviation is 47.88. Plots of my scores, Nicole’s scores, and the differences all look approximately normal. a) Which type of hypothesis test will you conduct? b) What are the requirements for this test? Are they met? c) State your null and alternative hypotheses. d) Find the appropriate test statistic. e) Find the critical value if you are testing at the 0.05 significance level. f) What do you conclude? 1
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A company keeps extensive records on its new salespeople on the premise that sales should increase with experience. A random sample of seven new salespeople produced the data on monthly sales and experience shown in the table below. Monthly sales (1000’s $) (y) Months on the Job (x) 2.4 2 7.0 4 11.3 8 15.0 12 0.8 1 3.7 5 12.0 9 The regression of sales on months produced the following output: a) Is there a significant relationship between monthly sales and months on the job? b) What level of monthly sales would you predict for an employee who had seven months on the job? c) What proportion of the variability in sales can be explained by the number of months on the job? d) What level of monthly sales would you predict for an employee who had five years on the job? e) Which would be widest? a) a 95% prediction interval at x=12 b) a 90% prediction interval at x=7 c) a 95% prediction interval at x=7 d) a 99% prediction interval at x=12 2
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Every time that Paul McCartney performs “Hey Jude” live, it has a slightly different length (largely depending on how many times he repeats the “Na na na na” refrain at the end of the song). Suppose that the length of the performance is normally distributed. In publicity material, Paul McCartney has claimed that his performance of “Hey Jude” tends to last “nine minutes or longer.” You are an investigative music critic for Pitchforkmedia.com, and have been assigned the task of trying to debunk Sir McCartney’s claim - you believe that, while some performances may last as long as he claims, on average, the performances are actually shorter. You randomly attend 25 Paul McCartney concerts, and record the length, in minutes, of each performance of “Hey Jude.” Your observations give you an average song length of 8 6 x . = minutes and a variance of 2 5 s . = . Test whether your belief that his average performance is less than nine minutes is correct.
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