Problem 1
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. a) Apples: weight in grams, weight in ounces b) Apples: circumference (inches), weight (ounces) c) College freshmen: shoe size, grade point average d) Gasoline: number of miles you drove since filling up, gallons remaining in your tank
Problem 2
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. a) T-shirts at a store: price each, number sold b) Scuba diving: depth, water pressure c) Scuba diving: depth, visibility d) All elementary school students: weight, score on a reading test
Problem 3
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. a) When climbing mountains: altitude, temperature b) For each week: ice cream cone sales, air-conditioner sales c) People: age, grip strength d) Drivers: blood alcohol level, reaction time
Problem 4
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. a) Long-distance calls: time (minutes), cost b) Lightning strikes: distance from lightning, time delay of the thunder c) A streetlight: its apparent brightness, your distance from it d) Cars: weight of car, age of owner
Problem 13
Politics, A candidate for office claims that "there is a. correlation between television watching and crime." Criticize this statement on statistical grounds.
Problem 14
Car thefts. The National Insurance Crime Bureau reports that Honda Accords, Honda Civics, and Toyota Camrys are the cars most frequently reported stolen, while Ford Tauruses, Pontiac Vibes, and Buick LeSabres are stolen least often. Is it reasonable to say that there's a correlation between the type of car you own and the risk that it will be stolen?
Problem 15
Roller coasters. Roller coasters get all their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. Here's a scatterplot of top Speed and largest Drop for 75 roller coasters around the world. a) Does the scatterplot indicate that it is appropriate to calculate the correlation? Explain. b) In fact, the correlation of Speed and Drop is \(0.91\). Describe the association.
Problem 20
Association. A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation. He had expected to find a fairly strong association, yet the correlation was near 0 . Discouraged, he didn't bother making a scatterplot. Explain to him how the scatterplot could still reveal the strong association he anticipated.
Problem 21
Prediction units. The errors in predicting hurricane tracks (examined in this chapter) were given in nautical miles. An ordinary mile is \(0.86898\) nautical miles. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in miles rather than nautical miles. Explain why converting the errors to miles would not change the correlation between Prediction Error and Year.
Problem 23
Correlation errors. Your Economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as Life Expectancy, Literacy Rate, etc.) for a few countries and reports to the class. Apparently, some of your classmates do not understand Statistics very well because you know several of their conclusions are incorrect. Explain the mistakes in their statements below. a) "My very low correlation of \(-0.772\) shows that there is almost no association between \(G D P\) and Infant Mortality Rate." b) "There was a correlation of \(0.44\) between \(G D P\) and Continent."
