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Chapter 4 Review – Statistics Honors Directions: 1.) Suppose the correlation between two variables x and y is due to the fact that both are responding to changes in some unobserved third variable. What is this due to? (a) (c) (e) 2.) cause and effect between x and y extrapolation none of the above (b) (d) the effect of the lurking variable common sense Suppose a straight line is fit to data having response variable y and explanatory variable x. Predicting values of y for values x outside the range of observed data is called: (a) (d) 3.) Circle the letter that best answers the question. correlation sampling (b) (e) causation none of the above (c) extrapolation Given the data points below. x y 1 5.3 2 7.6 3 11.0 4 16.0 5 24.1 6 33.8 7 43.4 Which of the following transformations to the data will change the scatterplot of the data to a straight line? *Hint: You must fill in the 4 lists and then look at the different scatterplots to find the most linear (or look at the r values) (a) (c) (e) Directions: 4.) take the log of x and the log of y take the log of y none of the above (b) (d) take the log of x no change is needed Fill in the blank to best complete each statement. A two-way table of counts describes the relationship between two ___________________ _______________________. 5.) _______________________ distributions look at one of the variables in comparison to the entire table count. 6.) _______________________ distributions look at either one row or one column as the condition to the probability. Page 1 of 4 Chapter 4 Review – Statistics Honors Directions: A researcher suspected a relationship between people preferences in movies and preference in pizza. A random sample of 100 people produced the following two – way table: Favorite Movie 7.) Show all required work to answer the question. Pizza Topping Preference Pepperoni Ground Beef Mushrooms 20 5 10 Jurassic Park Lethal Weapon I 8 15 12 Gone With the Wind 15 2 13 (a) Enter the counts on the table. (b) Find each of the following probabilities, in percents: (c) (d) i.) P pepperoni iv.) P(Jurassic ParkMushrooms) ii.) P ground beef v.) What is the marginal distribution of: (in percents) i.) Jurasic Park ii.) Lethal Weapon I iii.) Gone with the wind What is the conditional distribution of: (in percents) i.) Jurasic Park given pepperoni ii.) Gone with the wind given ground beef iii.) Mushrooms given Lethal Weapon I Page 2 of 4 iii.) P mushrooms P(Ground BeefLethal Weapon I) Chapter 4 Review – Statistics Honors * For #8-10, decide if there are any lurking variables that may be impacting the relationship. Write down what x, y, and z are, draw a diagram of the relationship, and then state whether the problem represents causation, common response, or confounding. Remember, there are many different answers to these problems. 8.) 9.) 10.) Research shows there is a strong positive correlation between ice cream consumption and murder rates. (a) Draw a diagram of the relationship and identify all variables. (b) This problem represents causation, common response, or confounding? ____________________ A soccer coach wanted to improve the team's playing ability, so he had them run two miles a day. At the same time the players decided to take vitamins. In two weeks the team was playing noticeably better, but the coach and players did not know whether it was from the running or the vitamins. (a) Draw a diagram of the relationship and identify all variables. (b) This problem represents causation, common response, or confounding? ____________________ Over the past 30 years in the United States there has been a strong positive correlation between cigarette sales and the number of high school graduates. (a) Draw a diagram of the relationship and identify all variables. (b) This problem represents causation, common response, or confounding? ____________________ Page 3 of 4 Chapter 4 Review – Statistics Honors 11.) George was doing a science experiment and determined that the population of fruit flies is described by the equation: log( population ) 2.6 .02( time in days ) Based on this equation, what is the approximate population of fruit flies in 30 days? Hint: You will have to rearrange the given equation to “get rid of” the log. 12.) The number of motor vehicles registered (in millions) in the U.S has grown as follows: Year (x) Vehicles (y) Year Vehicles 1940 1945 1950 1955 1960 32.4 31.0 49.2 62.7 73.9 1965 1970 1975 1980 1985 90.4 108.4 132.9 155.8 171.7 (a) Plot the number of vehicles against time on your calculator (don’t forget to change the years to year #). Assume the curved growth pattern exhibited is exponential. (b) Write the transformed LSRL and then use inverse transformations to transform the equation into an exponential equation. 13.) A curious thing happened to two baseball players this year during the first two weeks of the season. Here are the data : Weekly Results Week 1 2 At bats 5 20 Player 1 Hits 2 5 Batting Avg. At bats 25 5 Player 2 Hits 9 1 Batting Avg. (a) Show that each week, Player 1 had a higher batting average than does Player 2. (Fill in table above) (b) Show that at the end of the two weeks, the cumulative results for Player 2 were better than the cumulative results for Player 1. (c) What is the name for this apparent contradiction? ___________________________________ Page 4 of 4