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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. 77 (page 482)

Exercises 77 refer to the following setting. In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) that is unemployed. Here are estimates from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people.
Unemployment (1.1) Find the unemployment rate for people with each level of education. Is there an association between unemployment rate and education? Explain your answer.

Short Answer

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Explanation for correct option

The number of persons who are unemployed is equal to the number of individuals who are employed.

the unemployment rate is

It has been found that the unemployment rate varies depending on the highest level of education. As a result, there appears to be a link between unemployment and schooling.

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Most popular questions from this chapter

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is and the standard deviation of the loss is $σ = \(5000 .$ The distribution of losses is strongly right-skewed: many policies have $\) 0$ loss, but a few have large losses. The company hopes to sell $1000$ of these policies for $\(300$ each.

a. Assuming that the company’s claim is true, what is the probability that the mean loss from fire is greater than $\) 300$ for an SRS of $1000$ homeowners?

b. If the company wants to be $90 %$ certain that the mean loss from fire in an SRS of $1000$ homeowners is less than the amount it charges for the policy, how much should the company charge?

The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of $250$ square feet (ft² ) and a standard deviation of $2$ ft² . To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to be $x = 249.6 f t^{2}$ .

a. Find the probability that the sample mean area is $249.6 f t^{2}$ or less if the manufacturer’s claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average area of its aluminum foil rolls?

The candy machine Suppose a large candy machine has $45 %$ orange candies, Use Figures $7.11 a n d 7.12$ (page 434) to help answer the following questions.

(a) Would you be surprised if a sample of $25$ candies from the machine contained $8$ orange candies (that's $32 %$ orange)? How about $5$ orange candies ( $20 %$ orange)? Explain.

(b) Which is more surprising getting a sample of $25$ candies in which $32 %$ are orange or getting a sample of $50$ candies in which $32 %$ are orange? Explain.

Finch beaks One dimension of bird beaks is "depth"-the height of the beak where it arises from the bird's head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be Normally distributed with mean $μ = 9 .5 millimeters (mm)$ and standard deviation $σ = 1 .0 mm .$

a. Choose an SRS of 5 Medium Ground Finches from this population. Describe the sampling distribution of $\bar{x} .$

b. Find the probability that $\bar{x}$ estimates $μ$ within $\pm 0.5 mm$ . (This is the probability that $\bar{x}$ takes a value between 9 and 10 mm.

c. Choose an SRS of 50 Medium Ground Finches from this population. Now what is the probability that $\bar{x}$ falls within $\pm 0 .05 mm$ of $μ$ ? In what sense is the larger sample "better"?

The number of flaws per square yard in a type of carpet material varies with mean $1.6$ flaws per square yard and standard deviation flaws per square yard.

a. Without doing any calculations, explain which event is more likely:

randomly selecting a $1$ square yard of material and finding 2 or more flaws
randomly selecting $50$ square yards of material and finding an average of $2$ or more flaws

b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).

c. Calculate the probability of the second event in part (a).

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