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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 12: Q. 18 (page 792)

The professor swims Here are data on the time (in minutes) Professor Moore takes to swim $2000$ yards and his pulse rate (beats per minute) after swimming on a random sample of $23$ days:
Is there convincing evidence of a negative linear relationship between Professor Moore’s swim time and his pulse rate in the population of days on which he swims $2000$ yards?

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Most popular questions from this chapter

Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains $10$ identical hummingbird feeders and fills $5$ , chosen at random, with store-bought food from concentrate and the other 5 with a mixture of sugar and water. The feeders are then randomly assigned to $10$ possible hanging locations in the researcher’s yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on the amount consumed?

a. A one-sample $z -$ test for a proportion

b. A two-sample $z -$ test for a difference in proportions

c. A chi-square test for independence

d. A two-sample t-test

e. A paired t-test

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” 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’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

Nicole and Elena wanted to know if listening to music at a louder volume negatively impacts test performance. To investigate, they recruited $30$ volunteers and randomly assigned $10$ volunteers to listen to music at $30$ decibels, $10$ volunteers to listen to music at $60$ decibels, and $10$ volunteers to listen to music at $90$ decibels. While listening to the music, each student took a 10-question math test. Here is computer output from a least-squares regression analysis using role="math" localid="1654167255833" $x = volume$ and $y = number$ correct:

$Predictor Coef SE Coef T P Constant 9.9000 0.7525 13.156 0.0000 Volume - 0.0483 0.0116 - 4.163 0.0003 S = 1.55781 R - Sq = 38.2 % R - Sq (adj) = 36.0 %$

Is there convincing evidence that listening to music at a louder volume hurts test performance? Assume the conditions for inference are met.

Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let $X =$ the number of rolls required to obtain a sum greater than $7$ . If $100$ trials are conducted, which of the following is most likely to be the result of the simulation?

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$ students was selected from a large high school. For each student, $x = f o o t l e n g t h$ and $y = h e i g h t$ were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

The slope $β_{1}$ of the population regression line describes

a. the exact increase in height (cm) for students at this high school when foot length increases by $1$ .

b. the average increase in foot length(cm) for students at this high school when height increases by $1$ .

c. the average increase in height (cm) for students at this high school when foot length increases by $1$ .

d. the average increase in foot length (cm) for students in the sample when height increases by $1$

e. the average increase in height(cm) for students in the sample when foot length increases by $1$

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