Math 102 Quiz 2 Spring 2003 Hartlaub Name The point values for each part are listed in parentheses Solve all problems and show your work to receive the maximum amount of points Good luck and have a great break Part I Multiple Choice Problems Each question is worth 5 points 1 The Current Population Survey records the incomes of a large sample of American households To briefly describe the distribution of household income it is best to use a the mean and standard deviation b the mean and median c the five number summary d a regression line 2 Some people buy the stock of small companies The Russell 2000 Index which tracks the price of such shares was 648 on July 15 1999 On October 15 the index was 415 What percent decrease is this a 156 b 64 c 56 d 36 3 Which of these is not true of the correlation r between the lengths in inches and weights in pounds of a sample of brook trout a r must take a value between 1 and 1 b r is measured in inches c If longer trout tend to also be heavier then r 0 d r would not change if we measured these trout in centimeters instead of inches e Both b and d 4 You calculate the correlation between height and weight for a simple random sample of 50 students from Kenyon College Another student does the same for a simple random sample of 200 students from Kenyon College The other student should get 1 a a correlation greater than one b a correlation less than minus one c a higher value for the correlation d a lower value for the correlation e about the same value for the correlation 5 Suppose that the least squares regression line for predicting y from x is y 100 1 3x Which of the following is a possible value for the correlation between y and x a 1 3 b 1 3 c 0 d 0 5 e 0 5 6 The heights of a random sample of students in this class were recorded in inches They were then converted to the metric scale using the fact that one inch is the same as 2 54 centimeters What is the correlation between the heights in inches and the heights in centimeters a cannot be determined from the information given b 2 54 c 0 5 d 1 0 e 1 0 7 The March 2000 CPI 1982 84 100 was 171 but the component of the CPI for television sets was 52 There were great improvements in quality and features in television sets between 1982 84 and 2000 We can say that a the actual average price of television sets in 2000 was only 52 of the average price in 1982 84 2 b The actual average price of television sets in 2000 was 171 of the average price in 1982 84 c If a television sold for 100 is 1982 84 that same set would sell for only 52 in 2000 d Both a and c are true 8 In addition to national CPIs the BLS publishes separate CPIs for 29 large metropolitan areas These local CPIs are considerably less precise that is they have considerably more sampling variation This is because a of variation in prices among these metropolitan areas b the monthly CPI sample size within each metropolitan area is much smaller than the national sample size c the monthly CPI sample sizes within the metropolitan areas are not proportional to their population sizes d the metropolitan areas are not randomly selected e of variation in weather conditions among these metropolitan areas 9 A student doing a science fair project tries to germinate tomato seeds at different soil temperatures She writes I planted 10 seeds at each of three temperatures I found that 20 germinated at 55o 40 germinated at 60o and 37 germinated at 65o Why must her report be wrong a 37 is not a possible percent in this situation b The three percents given don t add to 100 c It s wrong to report percents she should report the correlation r d This isn t a randomized comparative experiment e It isn t possible for fewer seeds to germinate at 60o than at 65o 10 There is a close relationship between the correlation r and the slope b of the least squares regression line In particular it is true that a r and b always have the same sign which shows whether the variables are positively or negatively associated b r and b both always take values between 1 and 1 3 c the slope b is always at least as large as the correlation d the slope b is always equal to r2 the square of the correlation e both a and b are true 11 Suppose that the correlation between the scores of students on Exam 1 and Exam 2 in a statistics class is r 0 7 One way to interpret r is to say what percent of the variation in Exam 2 scores can be explained by the straight line relationship between Exam 2 scores and Exam 1 scores This percent is a 84 b 70 c 49 d 30 12 Consider a large number of countries around the world There is a positive correlation between the number of Nintendo games per person x and the average life expectancy y Does this mean that we could increase the life expectancy in Rwanda by shipping Nintendo games to that country a Yes the correlation says that as Nintendos go up so does life expectancy b No if the correlation were negative we could accept that conclusion but this correlation is positive c Yes positive correlation means that if we increase x then y will also increase d No the positive correlation just shows that richer countries have both more Nintendos and higher life expectancy e It makes no sense to calculate the correlation between these variables 13 The least squares regression line for predicting the percent of a country s females who are illiterate from the percent of males who are illiterate is female 3 34 1 39 x male In China 10 1 of men are illiterate Predict the percent of illiterate women in China a 4 6 b 14 4 c 17 4 d 47 8 14 The equation of the regression line in question 13 tells us that on the average when the male illiteracy rate goes up by 1 the female rate goes up by a 4 73 b 3 34 c 1 95 d 1 39 5 15 In government data a household consists of all occupants of a dwelling unit Choose an American household at random and count the number of people it contains Here is the assignment of probabilities for your outcome Number of 1 Persons 2 3 Probability 0 25 0 32 4 5 6 0 07 0 03 7 0 01 The probability of finding 3 people in a household is the same as the probability of finding 4 people These probabilities are marked in the table of the …