# Test explain your reasoning 0 45000 90000 135000

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Chapter 3 / Exercise 35
Modern Business Statistics with Microsoft Excel
Anderson/Sweeney
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test? Explain your reasoning. 0 45000 90000 135000 180000 0 5 10 Cleveland, OH Total personal income 0 45000 90000 135000 180000 0 5 10 Sacramento, CA Cleveland, OH Mean \$ 35,749 SD \$ 39,421 n 21 Sacramento, CA Mean \$ 35,500 SD \$ 41,512 n 17 6.24 Oscar winners. The first Oscar awards for best actor and best actress were given out in 1929. The histograms below show the age distribution for all of the best actor and best actress winners from 1929 to 2012. Summary statistics for these distributions are also provided. Is a t test appropriate for evaluating whether the difference in the average ages of best actors and actresses might be due to chance? Explain your reasoning. 33 20 40 60 80 0 10 20 Best actress Ages (in years) 20 40 60 80 0 10 20 Best actor Best Actress Mean 35.6 SD 11.3 n 84 Best Actor Mean 44.7 SD 8.9 n 84 33 data:oscars .
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Chapter 3 / Exercise 35
Modern Business Statistics with Microsoft Excel
Anderson/Sweeney
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290 CHAPTER 6. INFERENCE FOR NUMERICAL DATA 6.25 Friday the 13 th , Part I. In the early 1990’s, researchers in the UK collected data on traffic flow, number of shoppers, and traffic accident related emergency room admissions on Friday the 13 th and the previous Friday, Friday the 6 th . The histograms below show the distribution of number of cars passing by a specific intersection on Friday the 6 th and Friday the 13 th for many such date pairs. Also given are some sample statistics, where the difference is the number of cars on the 6th minus the number of cars on the 13th. 34 6th 120000 125000 130000 135000 140000 -1 0 1 13th 120000 125000 130000 135000 -1 0 1 Diff. 1000 2000 3000 4000 -1 0 1 6 th 13 th Diff. ¯ x 128,385 126,550 1,835 s 7,259 7,664 1,176 n 10 10 10 (a) Are there any underlying structures in these data that should be considered in an analysis? Explain. (b) What are the hypotheses for evaluating whether the number of people out on Friday the 6 th is different than the number out on Friday the 13 th ? (c) Check conditions to carry out the hypothesis test from part (b). (d) Calculate the test statistic and the p-value. (e) What is the conclusion of the hypothesis test? (f) Interpret the p-value in this context. (g) What type of error might have been made in the conclusion of your test? Explain. 6.26 Diamonds, Part I. Prices of diamonds are determined by what is known as the 4 Cs: cut, clarity, color, and carat weight. The prices of diamonds go up as the carat weight increases, but the increase is not smooth. For example, the difference between the size of a 0.99 carat diamond and a 1 carat diamond is undetectable to the naked human eye, but the price of a 1 carat diamond tends to be much higher than the price of a 0.99 diamond. In this question we use two random samples of diamonds, 0.99 carats and 1 carat, each sample of size 23, and compare the average prices of the diamonds. In order to be able to compare equivalent units, we first divide the price for each diamond by 100 times its weight in carats. That is, for a 0.99 carat diamond, we divide the price by 99. For a 1 carat diamond, we divide the price by 100. The distributions and some sample statistics are shown below.