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Chapter 7: Q. 23 (page 456)

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

Short Answer

Expert verified

xis an unbiased estimator of 渭if total of all conceivable mean values equals 渭

Step by step solution

01

Given Information

We need to explain how xis an unbiased estimator of渭.

02

Explanation

xis an unbiased estimator of 渭if total of all conceivablexis equal to渭. xisn't systematically higher or lower than; in other words, it doesn't have a strong propensity to underestimate or overestimate.

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Most popular questions from this chapter

The math department at a small school has 5teachers. The ages of these teachers are 23,34,37,42,58. Suppose you select a random sample of 4teachers and calculate the sample minimum age. Which of the following shows the sampling distribution of the sample minimum age?

a.

b.

c.

d.

e. None of these

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72%said they had voted in the election. Election records show that only 56%of registered voters voted in the election. Which of the following statements is true?

a. 72%is a sample; 56%is a population.

b. 72%and 56%are both statistics.

c. 72%is a statistic and 56%is a parameter.

d. 72%is a parameter and 56%is a statistic.

e. 72%and 56%are both parameters.

Songs on an iPod 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. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time x-x炉of these songs.

a. Identify the mean of the sampling distribution of x-x炉.

b. Calculate and interpret the standard deviation of the sampling distribution of x-路x炉. Verify that the 10%condition is met.

The number of undergraduates at Johns Hopkins University is approximately 2000 , while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about 3%of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80 at both schools. Which of the following is the best conclusion?

a. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it comes from a smaller population.

b. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it is based on a smaller sample size.

c. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it comes from a larger population.

d. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it is based on a larger sample size.

e. We expect that the estimate from Johns Hopkins will be about the same distance from the truth as the estimate from Ohio State because both samples are 3 % of their populations.

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.
See all solutions

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