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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.

Short Answer

Expert verified

(a) A graph for sample size of 1,2,3,4, and 5 as:

(b) It is clear as the sample size increases; there is decrease in the sampling error.

(c) A table similar to table 7.4 as:

Sample size
Number of samples
Number of samples within 1 of μ
Percentage of samples within 1 of μ
Number of samples within 2 of μ
Percentage of samples within 2 of μ
1
5
0
0
1
20
2
10
4
40
7
70
3
10
5
50
8
80
4
5
3
60
5
100
5
1
1
1
1
100

Step by step solution

01

Part (a) Step 1: Given information

To construct a graph that similar to the sample size of 1,2,3,4and 5.

02

Part (a) Step 2: Explanation

For the supplied population, use MINITAB to create dot plots for samples of size 1,2,3,4,and 5

MINITAB's procedure is as follows:

Step 1: Select Graph > Dotplot from the drop-down menu.

Step 2: Select Multiple Y's from the drop-down menu and click OK.

Step 3: In Graph variables, input columns ofn=1,n=2,n=3,n=4,n=5,

Step 4: Select OK.

MINITAB's output is as follows:

03

Part (b) Step 1: Given information

To illustrate the graph in part (a) about the impact of increasing sample size on sampling error.

04

Part (b) Step 2: Explanation

For five players, the average height(μ)is 78.6inches.

It is obvious from the MINITAB result in portion (a) that as the sample size grows, the sampling error decreases.
As a result, the sampling error has decreased.

05

Part (c) Step 1: Given information

To construct a table, that similar to table 7.4 for some values of own choice.

06

Part (c) Step 2: Explanation

Create a table with columns for the number of samples, the number of samples within 1of μ, the percentage of samples within 1of μ, the number of samples within2of μ, and the percentage of samples within2of μ.

Sample size
Number of samples
Number of samples within 1 of μ
Percentage of samples within 1 of μ
Number of samples within 2 of μ
Percentage of samples within 2 of μ
1
5
0
0
1
20
2
10
4
40
7
70
3
10
5
50
8
80
4
5
3
60
5
100
5
1
1
1
1
100

As a result, the table is generated.

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Most popular questions from this chapter

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

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 localid="1652592045497" 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.

Suppose that a simple random sample is taken without replacement from a finite population of size N.

Part (a): Show mathematically that Equations (7.1) and (7.2) are identical for samples of size 1.

Part (b): Explain in words why part (a) is true.

Part (c): Without doing any computations, determine r for samples of size N without replacement. Explain your reasoning.

Part (d): Use Equation(7.1) to verify your answer in part (c).

7.47 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 is3369 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 size400.

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

a. Determine the population mean height, μ, of the five players:

b. Consider samples of size 2 without replacement. Use your answer to Exercise 7.11(b) on page 295 and Definition 3.11 on page 140 to find the mean, μx¯, of the variable x¯.

c. Find μx¯using only the result of part (a).

Women at Work. In the article "Job Mobility and Wage Growth" (Monthly Labor Review. Vol. 128. No. 2, pp. 33-39).

A. Light examined data on employment and answered questions regarding why workers separate from their employers. According to the article, the standard deviation of the length of time that women with one job are employed during the first 8 years of their career is 92 weeks. Length of time employed during the first 8 years of a career is a left-skewed variable. For that variable, do the following tasks.

a. Determine the sampling distribution of the sample mean for simple random samples of 50 women with one job. Explain your reasoning.

b. Obtain the probability that the sampling error made in estimating the mean length of time employed by all women with one job by that of a random sample of 50 such women will be at most 20 weeks.

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