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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

In a recent poll, randomly selected New York State residents at various fast-food restaurants were asked if they supported or opposed a "fat tax" on sugared soda. Thirtyone percent said that they were in favor of such a tax and 66% were opposed. But when asked if they would support such a tax if the money raised were used to fund health care given the high incidence of obesity in the United States, $48 %$ said that they were in favor and $49 %$ were opposed.
(a) In this situation, explain how bias may have been introduced based on the way the questions were worded and suggest a way that the questions could have been worded differently in order to avoid this bias.
(b) In this situation, explain how bias may have been introduced based on the way the sample was taken and suggest a way that the sample could have been obtained in order to avoid this bias.
(c) This poll was conducted only in New York State. Suppose the pollsters wanted to ensure that estimates for the proportion of people who would support a tax on sugared soda were available for each state as well as an overall estimate for the nation as a whole. Identify a sampling method that would achieve this goal and briefly describe how the sample would be taken.

Do taller students require fewer steps to walk a fixed distance? The scatterplot shows the relationship between x=height (in inches) and y=number of steps required to walk the length of a school hallway for a random sample of 36 students at a high school.

A least-squares regression analysis was performed on the data. Here is some computer output from the analysis

a. Describe what the scatterplot tells you about the relationship between height and the number of steps.

b. What is the equation of the least-squares regression line? Define any variables you use.

c. Identify the value of each of the following from the computer output. Then provide an interpretation of each value.

i. $b_{0}$

ii. $b_{1}$

iii. s

iv. $S E b_{1}$

If $P (A) = 0.24$ and $P (B) = 0.52$ and events $A$ and $B$ are independent, what is $P (A$ or $B)$ ?

а. $0.1248$

b. $0.28$

c. $0.6352$

d. $0.76$

e. The answer cannot be determined from the given information.

A set of $10$ cards consists of $5$ red cards and $5$ black cards. The cards are shuffled thoroughly, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This is done a total of four times. Let X be the number of red cards observed in these four trials. The random variable X has which of the following probability distributions?

a. The Normal distribution with mean $2$ and standard deviation $1$

b. The binomial distribution with $n = 10$ and $p = 0.5$

c. The binomial distribution with $n = 5$ and $p = 0.5$

d. The binomial distribution with $n = 4$ and $p = 0.5$

e. The geometric distribution with $p = 0.5$

Prey attracts predators . Here is computer output from the least-squares regression analysis of the perch data

a. What is the estimate for $β 0$ ? Interpret this value.

b. What is the estimate for $β 1$ ? Interpret this value.

c. What is the estimate for $σ$ ? Interpret this value.

d. Give the standard error of the slope $S E b 1$ . Interpret this value.

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