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Chapter 7: Q.20 (page 431)

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 M in this population.

(a) Explain to someone who knows no statistics what it means to say that xis an unbiased estimator of 渭.

(b) The sample result x is an unbiased estimator of the population mean 渭 no matter what size SRS the study chooses. Explain to someone who knows no statistics why a large random sample gives more trustworthy results than a small random sample.

Short Answer

Expert verified

a). The average of all possible x炉-values is equal to 渭.

b). A larger sample gives more information and less variability.

Step by step solution

01

Part (a) Step 1: Given Information

A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds.

02

Part (a) Step 2: Explanation

x炉is an unbiased estimator of 渭if the average of all possible values of x炉is equal to 渭.

03

Part (b) Step 1: Given Information

A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds.

04

Part (b) Step 2: Explanation 

A larger sample gives more information about the distribution of values and thus it can be used to make more precise estimates.

More precise results also have less variability in the results.

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Most popular questions from this chapter

About 75%of young adult Internet users (ages 18 to 29) watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion p^in this sample who watch online video.

4. If the sample size were 9000 rather than 1000 , how would this change the sampling distribution of p^?

Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in3%such operations, the repair fails in 14%, and both infection and failure occur together 1%at the time. What is the probability that the operation is successful for someone who has an operation that is free from infection?

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The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. 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=0.80at both schools. Which of the following is the best conclusion?

(a) The estimate from Johns Hopkins has less sampling variability than that from Ohio State.

(b) The estimate from Johns Hopkins has more sampling variability than that from Ohio State.

(c) The two estimates have about the same amount of sampling variability.

(d) It is impossible to make any statement about the sampling variability of the two estimates since the students surveyed were different.

(e) None of the above

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(a) Describe how you would use Table D at line 111 to choose an SRS of 3 of these reptiles to study.

(b) Use your method from part (a) to select your sample. Identify the reptiles you chose.

Desert tortoise Green sea turtle Loggerhead sea turtle Giant garter snake Olive Ridley sea turtle Leatherback sea turtle Barefoot banded gecko San Francisco garter snake Island night lizard Alameda whip snake Coachella Valley fringe-toed lizard Flat-tailed horned lizard Southern rubber boa blunt-nosed leopard lizard

More on insurance An insurance company knows that in the entire population of homeowners, the mean annual loss from 铿乺e is 渭=250and the standard deviation of the loss is 蟽=300. The distribution of losses is strongly right-skewed: many policies have 0loss, but a few have large losses. If the company sells 10,000 policies, can it safely base its rates on the assumption that its average loss will be no greater than 275? Follow the four-step process
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