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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 7: Q 49. (page 464)

The sampling distribution of $\hat{p}$ is approximately Normal because
a. there are at least $7500$ Division I college athletes.
b. $n p = 225$ and $n (1 - p) = 525$ are both at least $10$
c. a random sample was chosen.
d. the athletes’ responses are quantitative.
e. the sampling distribution of p^ always has this shape.

Short Answer

Expert verified

The correct option is (b) $n p = 225$ and $n (1 - p) = 525$ are both at least 1 $10$

Step by step solution

01

Given information

p = 30 % = 0.30 n = 750

02

Calculation

$n p = 750 (0.30) = 225 n (1 - p) = 750 (1 - 0.30) = 525$

Because both are at least $10$ and the sampling distribution of the sample fraction is approximately normal, the normal distribution is satisfied.

Hence, the correct option is (b)

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Most popular questions from this chapter

You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked to reveal her attitude toward the product. You think there may be large differences in the responses of women who are employed and those who are not. Because of these differences, you should use

a. a block design, but not a matched pairs design.

b. a completely randomized design.

c. a matched pairs design.

d. a simple random sample.

e. a stratified random sample.

Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution of $x^{- \bar{x}}$ to be 10 seconds? Justify your answer.

Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter $μ = 40.125$ millimeters (mm). The machine has some variability, so the standard deviation of the diameters is $σ = 0.002 mm$ . The machine operator inspects a random sample of 4 axles each hour for quality control purposes and records the sample mean diameter $x^{-} \bar{x}$ . Assume the machine is working properly.

a. Identify the mean of the sampling distribution of $x^{-} \cdot \bar{x}$ .

b. Calculate and interpret the standard deviation of the sampling distribution of $x^{-} \bar{x}$ .

Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent of U.S. families living in poverty (POV). Data were collected from all 50 states and the District of Columbia, and a regression analysis was conducted.

The resulting least-squares regression line is given by ${POV}^{\land} = 59.2 - 0.620$ (HSGR) $\hat{POV} = 59.2 - 0.620$ (HSGR) with $r 2 = 0.802 r^{2} = 0.802$ . Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?

a. For each 1% increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.896 .

b. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.802.

c. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.620.

d. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.802.

e. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.620.

Do you jog? The Gallup Poll asked a random sample of 1540 adults, "Do you happen to jog?" Suppose that the true proportion of all adults who jog is $p = 0.15$ . $p = 0.15$ .

a. What is the mean of the sampling distribution of $p \land \hat{p}$ ?

b. Calculate and interpret the standard deviation of the sampling distribution of $p^{\land \hat{p}}$ . Check that the $10 %$ condition is met.

c. Is the sampling distribution of $p^{\land \hat{p}}$ approximately Normal? Justify your answer.

d. Find the probability that between $13 % a n d 17 %$ of people jog in a random sample of 1540 adults.

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