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Chapter 12: Q. 20 (page 792)

Pencils and GPA Is there a relationship between a student鈥檚 GPA and the number of pencils in his or her backpack? Jordynn and Angie decided to find out by selecting a random sample of students from their high school. Here is computer output from a least-squares regression analysis using x=number of pencils and y=GPA:

Is there convincing evidence of a linear relationship between GPA and number of pencils for students at this high school? Assume the conditions for inference are met.

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Most popular questions from this chapter

Less mess? Kerry and Danielle wanted to investigate if tapping on a can of soda would reduce the amount of soda expelled after the can has been shaken. For their experiment, they vigorously shook 40cans of soda and randomly assigned each can to be tapped for 0seconds, 4seconds, 8seconds, or 12seconds. After opening the cans and waiting for the fizzing to stop, they measured the amount expelled (in milliliters) by subtracting the amount remaining from the original amount in the can. Here are their data:

Here is some computer output from a least-squares regression analysis of these data. Construct and interpret a 95%confidence interval for the slope of the true regression line.

Exercises T12.4鈥揟12.8 refer to the following setting. An old saying in golf is 鈥淵ou drive for show and you putt for dough.鈥� The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour鈥檚 world money list are examined. The average number of putts per hole (fewer is better) and the player鈥檚 total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
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T12.5 Suppose that the researchers test the hypotheses H0:尾1=0 versus

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Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10randomly selected bears. Here is some regression output for these data:

Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth?

a. 20.230卤1.695

b. 20.230卤3.83

c. 20.230卤3.91

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Click-through rates Companies work hard to have their website listed at the top of an Internet search. Is there a relationship between a website鈥檚 position in the results of an Internet search (1=top position,2=2nd position, etc.) and the percentage of people who click on the link for the website? Here are click-through rates for the top 10 positions in searches on a mobile device:

a. Make an appropriate scatterplot for predicting click-through rate from the position. Describe what you see.

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c. Perform least-squares regression on the transformed data. Give the equation of your regression line. Define any variables you use.

d. Use your model from part (c) to predict the click-through rate for a website in the 11th position.

Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean 4.5minutes and standard deviation 0.9minutes.

a. Find the probability that Marcella鈥檚 shower lasts between 3and 6minutes on a randomly selected day.

b. If Marcella took a 7minute shower, would it be classified as an outlier by the 1.5IQRrule? Justify your answer.

c. Suppose we choose 10days at random and record the length of Marcella鈥檚 shower each day. What鈥檚 the probability that her shower time is 7minutes or greater on at least 2of the days?

d. Find the probability that the mean length of her shower times on these 10 days exceeds5 minutes.
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