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Chapter 7: Q. T7.11 (page 487)

Here are histograms of the values taken by three sample statistics in several hundred samples from the same population. The true value of the population parameter is marked with an arrow on each histogram.

Which statistic would provide the best estimate of the parameter? Justify your answer

Short Answer

Expert verified

The resultant graph is

Step by step solution

01

Given Information

The given graphs

02

Explanation for correct option

The graph shows that the bars are centred around the value and have the least fluctuation (therefore the smallest overall width) (indicated by the arrow).

As a result, histogram A would lead to an excellent parameter estimation.

As a result, the best solution is (A)

03

Explanation for incorrect option

The option (b) and (c) is not the correct answer.

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Most popular questions from this chapter

Bad eggs Selling eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9 of these eggs had salmonella contamination. Identify the population, the parameter, the sample, and the statistic.

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

a. reduce the bias of the estimate.

b. increase the bias of the estimate.

c. reduce the variability of the estimate.

d. increase the variability of the estimate.

e. reduce the bias and variability of the estimate.

Dem bones (2.2) Osteoporosis is a condition in which the bones become brittle due to the loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in a standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD score that is 2.5standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and gender roughly follow a Normal distribution.

a. What percent of healthy young adults have osteoporosis by the WHO criterion?

b. Women aged 70to 79are, of course, not young adults. The mean BMD in this age group is about-2 on the standard scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population has osteoporosis?

Five books An author has written 5 children's books. The numbers of pages in these books are 64,66,71,73, and 76 .

a. List all 10 possible SRSs of size n=3,n=3, calculate the median number of pages for each sample, and display the sampling distribution of the sample median on a dotplot.

b. Describe how the variability of the sampling distribution of the sample median would change if the sample size was increased to n=4.n=4.

c. Construct the sampling distribution of the sample median for samples of size n=4. n=4. Does this sampling distribution support your answer to part (b)? Explain your reasoning.

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炉=810grams. This sample mean is an unbiased estimator of the mean weight 渭 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炉will equal 810 .

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

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

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

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