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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. 69 (page 481)

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

Short Answer

Expert verified

The statement explained by the student is wrong, because the histogram of sample values becomes more Normal as you take larger and larger samples from a population.

Step by step solution

01

Given information

The student made a statement "The histogram of the sample values looks more and more Normal when you take larger and larger samples from a population."

02

According to Question

It's incorrect because as the sample size grows, the histogram of sample values will take on the shape of the population distribution.

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Most popular questions from this chapter

Bad eggs Selling eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9 of these eggs had salmonella contamination. Identify the population, the parameter, the sample, and the statistic.

David’s iPod has about $10, 000$ songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of $225$ seconds and a standard deviation of $60$ seconds.

a. Describe the shape of the sampling distribution of $x$ for SRSs of size $n = 5$ from the population of songs on David’s iPod. Justify your answer.

b. Describe the shape of the sampling distribution of $x$ for SRSs of size $n = 100$ from the population of songs on David’s iPod. Justify your answer.

Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?

$a . 4 (16) 3 (56) 14 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1} b . (16) 3 (56) 1 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1} c . 4 (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3} d . (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3} e . 6 (16) 1 (56) 3^{6} {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$

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.

Which one of the following would be a correct interpretation if you have a z-score of $+ 2.0$ on an exam?

a. It means that you missed two questions on the exam.

b. It means that you got twice as many questions correct as the average student.

c. It means that your grade was 2 points higher than the mean grade on this exam.

d. It means that your grade was in the upper $2 %$ of all grades on this exam.

e. It means that your grade is 2 standard deviations above the mean for this exam.

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