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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


On one episode of his show, a radio show host encouraged his listeners to visit his website and vote in a poll about proposed tax increases. Of the 4821 people who vote, 4277 are against the proposed increases. To which of the following populations should the results of this poll be generalized?

a. All people who have ever listened to this show

b. All people who listened to this episode of the show

c. All people who visited the show host's website

d. All people who voted in the poll

e. All people who voted against the proposed increases

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-x¯=810grams. 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-x¯will equal 810 .

b. in all possible samples of size 219 from this population, the mean of the values of x-x¯will equal μ

c. as we take larger and larger samples from this population, x-x¯will get closer and closer to μ.

d. in all possible samples of size 219 from this population, the values of x-x¯will have a distribution that is close to Normal.

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

Tall girls According to the National Center for Health Statistics, the distribution of height for 16-year-old females is modeled well by a Normal density curve with mean μ=64inches and standard deviation σ=2.5inches. Assume this claim is true for the three hundred 16-year-old females at a large high school.

a. Make a graph of the population distribution.

b. Imagine one possible SRS of size 20from this population. Sketch a dotplot of the distribution of sample data.

Detecting gypsy moths The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed with a mean of 0.5 and a standard deviation of 0.7.

a. Explain why it is reasonable to use a Normal distribution to approximate the sampling distribution of x-x¯for SRSs of size 50 .

b. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

c. In a recent month, the mean number of moths in an SRS of size 50 was x-=0.6. x¯=0.6. Based on this result, is there convincing evidence that the moth population is getting larger in this state? Explain your reasoning.

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.
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