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Chapter 7: Q. 20 (page 456)

Sample minimums List all 6possible SRSS of size n=2, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased estimator of the population minimum? Explain your answer.

COLORAGE
RED1
WHITE5
SILVER8
RED20

Short Answer

Expert verified

The required dotplot is and sample proportion not an unbiased estimator of the population proportion.

Step by step solution

01

Given information

We need to find out the proportion of cars in the sample, display the sampling distribution of the sample proportion on a dotplot and whether the sample proportion is an unbiased estimator of the population proportion or not.

COLORAGE
RED1
WHITE5
SILVER8
RED20
02

Explanation

We know that

The sample proportion of all the red cars is equal to half of the no. of red cars in the sample.

Sample of size twoSample minimum
1,2
1
1,3
1
1,4
1
2,3
5
2,4
5
3,4
8

And the required dotplot is,


As the mean of sampling distribution is not equal to population proportion.

So, the sample proportion not an unbiased estimator of the population proportion.

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Most popular questions from this chapter

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.

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.

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

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 蟽=\(5000.The distribution of losses is strongly right-skewed: many policies have \)0loss, but a few have large losses. The company hopes to sell 1000 of these policies for \(300each.

a. Assuming that the company鈥檚 claim is true, what is the probability that the mean loss from fire is greater than \)300for 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?

Suppose that you have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you. Infection occurs in 3%of such operations, the repair fails in 14%, and both infection and failure occur together 1%of the time. What is the probability that the operation is successful for someone who has an operation that is free from infection?

a. 0.8342

b. 0.8400

c. 0.8600

d. 0.8660

e. 0.9900
See all solutions

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