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Chapter 7: Q.7.22 (page 296)

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 6construct a table similar to table 7.2 on page293 what is the relationship between the only possible sample here and the population?

(b) For a random sample of size 6determine the probability that themean wealth of the two people obtained will be within 3(i.e,3 billion) of the population mean. interpret your result in terms of percentages.

Short Answer

Expert verified

(a)

The relationship between the only possible sample here and the population is that both are equal.

(b) There is 100%chance that the mean wealth of the six people will be within 3billion of the population mean.

Step by step solution

01

Part (a) Step 1: Given Information 

Given in the question that,

we have to construct a table for sample size6

02

Part (a) Step2 : E xplanation

The sample size of 6and the corresponding means are obtained as shown in the below table :

The relationship between the only possible sample here and the population is that both are equal.

03

Part (b) Step 1: Given Information 

Given in the question that,

we have to deterrmine the probability that xis within 3billion ofμ.

04

Part(b) Step 2: Explanation 

We have to obtain P(μ-3≤x¯≤μ+3)

P(μ-3≤x¯≤μ+3)=P(46.5-3≤x¯≤46.5+3)

=P(43.5≤x¯≤49.5)

=11=1

Therefore, the probability that xis within 3billion ofμis1.

Interpretation:

There is100%chance that the mean wealth of the six people will be within 3billion of the population mean.

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Most popular questions from this chapter

7.54 Unbiased and Biased Estimators. A statistic is said to be an unbiased estimator of a parameter if the mean of all its possible values equals the parameter. otherwise, it is said to be a biased estimator. An unbiased estimator yields, on average, the correct value of the parameter, whereas a biased estimator does not.
a. Is the sample mean an unbiased estimator of the population mean? Explain your answer.
b. Is the sample median an unbiased estimator of the population median? (Hint: Refer to Example 7.2 on pages 292-293. Consider samples of size 2.)

Population data: 1,2,3,4,5

Part (a): Find the mean, μ, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 5construct a table similar to table 7.2 on page293.(There are 6 possible sample) of size 5

(b) For a random sample of size 5determine the probability that themean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean. interpret your result in terms of percentages.

Baby Weight. The paper "Are Babies Normal?" by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No, 4. pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard deviation of 581 grams.
a. Identify the population and variable.
b. For samples of size 200, find the mean and standard deviation of all possible sample mean weights.
c. Repeat part (b) for samples of size 400.

Population data: 2,3,5,5,7,8

Part (a): Find the mean, μ, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most0.5.
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