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Chapter 7: Q. 7.24 (page 296)

Suppose that a sample is to be taken without replacement from a finite population of size Nif the sample size is the same as the population size

(a) How many possible samples are there?

(b) What are the possible sample means?

(c) What is the relationship between the only possible sample and the population

Short Answer

Expert verified

Part a. Only one possible sample is there.

Part b. There is only one possible sample mean which is equal to the population mean.

Part c. The only possible sample is the same as the population itself.

Step by step solution

01

Part (a) Step 1. Given Information

It is given that a sample is to be taken without replacement from a finite population of size N if the sample size is the same as the population size.

We have to find out how many possible samples are there.

02

Part (a) Step 2. Explanation

We have a population of size N. And we have to draw a sample of size N without replacement.

There will be only one possible sample since we are drawing the sample without replacement and the sample size is equal to the population size.

So there is only one possible sample and it is the population itself.

03

Part (b) Step 1. Given Information

It is given that a sample is to be taken without replacement from a finite population of size N if the sample size is the same as the population size.

We have to find the total possible sample means.

04

Part (b) Step 2. Explanation

As there is only one possible sample and it is the population itself.

So there will be only one possible sample mean and it would be equal to the population mean itself.

05

Part (c) Step 1. Given Information

It is given that a sample is to be taken without replacement from a finite population of size N if the sample size is the same as the population size.

We have to find the relationship between the only possible sample and the population.

06

Part (c) Step 2. Explanation

As there is only one possible sample and it is the population itself.

So the relation between the only possible sample and the population is that they are the same.

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Most popular questions from this chapter

The following graph shows the curve for a normally distributed variable. Superimposed are the curves for the sampling distributions of the sample mean for two different sample sizes.

a. Explain why all three curves are centered at the same place.

b. Which curve corresponds to the larger sample size? Explain your answer.

c. Why is the spread of each curve different?

d. Which of the two sampling-distribution curves corresponds to the sample size that will tend to produce less sampling error? Explain your answer.

c. Why are the two sampling-distribution curves normal curves?

Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.

7.16 NBA Champs. This exercise requires that you have done Exercises 7.11-7.15.
a. Draw a graph similar to that shown in Fig. 7.3 on page 294for sample sizes of 1,2,3,4, and 5.
b. What does your graph in part (a) illustrate about the impact of increasing sample size on sampling error?
c. Construct a table similar to Table 7.4 on page 294 for some values of your choice.

The winner of the 2012-2013 National Basketball Association (NBA) championship was the Miami Heat, One possible starting lineup for that team is as follows:

Part (a): Find the population mean height of the five players.

Part (b): For samples of size 2, construct a table similar to Table 7.2 on page 293. Use the letter in parentheses after each player's name to represent each player.

Part (c): Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.

Part (d): For a random sample of size2, what is the chance that the sample mean will equal the population mean?

Part (e): For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be1 inch or less; that is, determine the probability that x will be within1 inch of 渭. Interpret your result in terms of percentages.

What is another name for the standard deviation of the variable x ? What is the reason for that name?
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