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Chapter 7: Q7.25 (page 296)

Suppose that a random sample of size 1is to be taken from a finite population of size N.

a. How many possible samples are there?

b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.

c. What is the difference between taking a random sample of size 1from a population and selecting a member at random from the population?

Short Answer

Expert verified

(a) Because each of the population's Nunits might be a random sample, there are Npossible samples.

(b) The sample means are exactly equivalent to the variable under consideration's possible observation.

(c) There is no change because the sample mean of a random sample of size is equal to the sample's single sample observation.

Step by step solution

01

Part (a) Step 1: Given Information 

Given in the question that sample of size 1is to be taken from a finite population of size Nwe have to find the total possible samples are there.

02

Part (a) Step 2: Explanation 

We have to draw a random sample of size 1from the population.

Because each of the Npopulation units can be a random sample, there are Npossible samples.

03

Part (b) Step 1: Given Information 

Given in the question that sample of size 1is to be taken from a finite population of size Nwe have to find the relationship between the possible sample means and the possible observations of the variable under consideration.

04

Part (b) Step 2: Explanation 

Nothing except the sample observation since mean of a single value to that value in a sample of size 1.

therefore, The sample means are exactly equivalent to the variable under consideration's possible observation.

05

Part (c) Step 1: Given Information 

Given in the question that sample of size 1is to be taken from a finite population of size N we have to find the difference between taking a random sample of size 1 from a population and selecting a member at random from the population.

06

Part (c) Step 2: Explanation 

There is no change because the sample mean of a random sample of size is equal to the sample's single sample observation.

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Most popular questions from this chapter

Taller Young Women. In the document Anthropometric Reference Data for Children and Adults, C. Fryer et al. present data from the National Health and Nutrition Examination Survey on a variety of human body measurements. A half-century ago, the mean height of (U.S.) women in their 20s was 62.6 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.88 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 25 of today"s women in their 20s have mean heights of at least 64.24 inches?

Population data: 1,2,3

Part (a): Find the mean, 渭,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.

What is the sampling distribution of a statistic? Why is it important?

7.35 Refer to Exercise 7.5 on page 295 .

a. Use your answers from Exercise 7.5(b) to determine the mean, 渭i. of the variable x炉 for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, 渭5, of the variable x炉, using only your answer from Exercise 7.5(a).

7.46 Young Adults at Risk. Research by R. Pyhala et al. shows that young adults who were born prematurely with very low birth weights (below 1500grams) have higher blood pressure than those born at term. The study can be found in the article. "Blood Pressure Responses to Physiological Stress in Young Adults with Very Low Birth Weight" (Pediatrics, Vol. 123, No, 2, pp. 731-734). The researchers found that systolic blood pressures, of young adults who were born prematurely with very low birth weights have mean 120.7mmHgand standard deviation 13.8mmHg.
a. Identify the population and variable.
b. For samples of 30 young adults who were born prematurely with very low birth weights, find the mean and standard deviation of all possible sample mean systolic blood pressures. Interpret your results in words.
c. Repeat part (b) for samples of size 90 .
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