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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

Dead battery? A car company claims that the lifetime of its batteries varies from car to car according to a Normal distribution with mean $μ = 48$ months and standard deviation $σ = 8 .2$ months. A consumer organization installs this type of battery in an SRS of 8 cars and calculates $\bar{x} = 42 .2$ months.

a. Find the probability that the sample mean lifetime is 42.2 months or less if the company's claim is true.

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

A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. Here is a cumulative relative frequency graph from data collected over the past year. According to the graph, the shortest $80 %$ of calls will take how long to complete?

a. Less than 10 minutes

b. At least 10 minutes

c. Exactly 10 minutes

d. At least $5.5$ minutes

e. Less than $5.5$ minutes

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was $x^{-} \bar{x} = 810$ grams. This sample mean is an unbiased estimator of the mean weight $μ$ in the population of all ELBW babies, which means that

a. in all possible samples of size 219 from this population, the mean of the values of $x^{-} \bar{x}$ will equal 810 .

b. in all possible samples of size 219 from this population, the mean of the values of $x^{- \bar{x}}$ will equal $μ$

c. as we take larger and larger samples from this population, $x^{- \bar{x}}$ will get closer and closer to $μ$ .

d. in all possible samples of size 219 from this population, the values of $x^{-} \bar{x}$ will have a distribution that is close to Normal.

e. the person measuring the children's weights does so without any error.

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"?

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of $13$ to $16$ year-olds. The researchers will report the mean $x$ from their sample as an estimate of the mean cholesterol level $μ$ in this population. Explain to someone who knows little about statistics what it means to say that $x$ is an unbiased estimator of $μ$ .

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