6.2 Problem Set

1) What are the two things that the correlation coefficient measures?

2) The program used to create this scatterplot found the line-of-best-fit and reported the r-squared value as r² = 0.805 for the relationship between arm-span and height for several individuals. What is the correlation coefficient? Is it positive or negative? Explain how you know.

3) During the summer Ms. Statsteacher lets her two daughters stay up later than during the school year. Their bedtimes during the summer range from 8:30 p.m. to 12:30 a.m. She has discovered that her older daughter Reily will wake up between 8:00 and 9:00 a.m. no matter what time she goes to bed. However, her younger daughter Neila tends to wake up later after she gets to stay up later, and earlier when she goes to bed earlier. Neila has been known to wake up anytime between 8:00 and 11:45 a.m.

a) Sketch a separate (approximate) scatterplot for each daughter, that compares time going to sleep and time waking up. Which will be explanatory and which will be response?

b) Which of these do you think will best approximate the correlation for Reily?

4) Suggest possible lurking variables to explain the high correlations between the following variables. Explain your reasoning. Consider whether common response, confounding, or coincidence may be involved.

a) As ice cream sales increase, the rate of drowning deaths increases sharply. Does this mean that ice cream causes drowning?

b) With a decrease in the number of pirates, there has been an increase in global warming over the same time period. Does this mean global warming is caused by a lack of pirates?

c) The higher the number of fire-fighters fighting a fire, the more damage done by the fire. Does this mean that we can limit damage by sending fewer fire-fighters to fires?

d) Suppose that each of the hockey players on the high school team supplies his or her own hockey stick, with varying degrees of flex. The assistant coach has been keeping a record of the degree of flex for each player's stick and their respective point totals (goals and assists). He has noted that there is a strong, negative correlation between these two variables. In other words, the players with less flex in their sticks are scoring more points and those with more flex are scoring fewer points. Does this prove that the amount of flex in a stick will cause the point totals for the players? Can we then give players less flexible sticks and expect to increase scoring?

5) In a recent study in Resource Manual, it was noted that divorced men were twice as likely to abuse alcohol as married men. The authors concluded that getting divorced caused alcohol abuse. Do you agree? Explain your reasoning.

6) A commercial for a new diet pill claims "You will lose weight while you sleep! No exercise needed!". They then show several before-and-after photos of people who have lost weight. People who were obese are now very buff. They then give the information for you to order the pills ("for three payments of just $19.95 each, plus shipping and handling"). Is this proof that these diet pills caused these people to lose weight? Suggest possible lurking variables. Explain your reasoning.

7) Match each graph with its correlation coefficient:

8) A correlation of r = 0 indicates no linear relationship between the two given variables. But, this does not mean that there is no relationship between the two variables. Sketch a scatterplot in which there is a strong relationship between the variables, but the correlation would be near r = 0.

9) Use the "Beach Visitors" scatterplot to answer the questions that follow.

Review Exercises

10) Zeke flips a coin 93 times and tails shows up 34 of those times. Based on these results, what is the experimental probability of getting tails?

11) If Stephanie's batting average is 0.258, how many hits would you expect her to get out of her next 20 times at bat?

12) You have been playing the game Yahtzee with some friends and you have been keeping track of how often someone gets a Yahtzee (5 of the same dice) when they roll all 5 dice at once. The results today have been 3 Yahtzee's, on a single roll, out of 79 trials. Based on these results, what is the experimental probability of getting a Yahtzee in one roll?

13) What is the theoretical probability of getting a Yahtzee in one roll?

Image Attributions

• [1]^ License: CC BY-NC 3.0
• [2]^ License: CC BY-NC 3.0
• [3]^ License: CC BY-NC 3.0
• [4]^ License: CC BY-NC 3.0
• [5]^ License: CC BY-NC 3.0
• [6]^ License: CC BY-NC 3.0
• [7]^ License: CC BY-NC 3.0
• [8]^ License: CC BY-NC 3.0
• [9]^ License: CC BY-NC 3.0
• [10]^ License: CC BY-NC 3.0

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