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stat101-hw2-solution

# stat101-hw2-solution - Solutions for STAT 101 Homework 2...

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Solutions for STAT 101, Homework 2 Professor Rakhlin Solutions prepared by Julie, Tung, and Wei October 6, 2011 Chapter 4, Problem 52 (a) The mean is 130 second with SD = 13 . 5 seconds.The usual notions of center and spread are not useful summaries of the data because it is not bell shaped. (b) The shape of the distribution is bi-modal, with one mode larger than the other. The data is skewed right. (c) Since most of the data is in the ﬁrst mode, I would expect the box to fall over the 1st mode and a lot of outliers to fall to the right of the box (the mean is greater than the median). (d) This distribution does not give us any information about the years in which these winning times oc- curred. What may have happened is that in the 1800s, the best times were around 150-160 seconds, and one year there was a horse that ran it in about 120. The level of the sport then highly increased, and from that year forth the best times were much faster than they used to be. Another reason is the bimodal shape is caused by a change in the length of the race. The races since 1896 have been shorter. Chapter 5, Problem 21 The answer is true since there is a diﬀerent hire rate for each gender. In other words, the conditional distributions of hiring given gender are diﬀerent. Hence, there is an association Chapter 5, Problem 24 (a) Find association would mean that the proportion of loans repaid was diﬀerent for smaller loans than for larger loans. (b) We look at the conditional distribution of loan payment given the size of the loan. We can obtain these numbers by dividing each cell by the total number of loans for each row. For example, for the cell containing the large, repaid loans, we divide it, 40, by the total number of large loans, 50, and multiply by 100 to obtain 80%,

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stat101-hw2-solution - Solutions for STAT 101 Homework 2...

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