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Chapter 7: Q. 7.15 (page 295)

Repeat parts (b)-(e) of Exercise 7.11 for samples of size5.

Short Answer

Expert verified
  1. Part (b): Constructing the table of samples of size 5 of the given population is given below,


Part (c): The dot plot is given below,


Part (d): The chance that sample mean is equal to population mean is 1.

Part (e): The probability that x is within 1 inch of 渭is 1.

On interpreting, there is 100% change that the mean height of the four players selected will be within 1 inch of the population mean.

Step by step solution

01

Part (b) Step 1. Given information

Consider the given question,

02

Part (b) Step 2. Construct samples of size 5 of the given population.

The samples of size 5 and the corresponding means are obtained,

Here, Chrish Bosh by B, Dwyane Wade by W, LeBron James by J, Mario Chalmers by C and Udonis Haslem H.

03

Part (c) Step 1. Construct the dot plot.

On constructing the dot plot for the sampling distribution of the sample mean,

04

Part (d) Step 1. Find the chance that the sample mean will equal the population mean.

Consider the previous question,

The population mean height for five players is 7.86inches.

From table obtained in part (b), it is clear that none of the sample means are equal to the population mean. Also, number of samples of size 5is 1.

Px=渭=11=1

05

Part (e) Step 1. Find the probability that xwill be within 1 inch of μ.

We need to find the P渭-1鈮�x鈮�渭+1.

From the table obtained in part (b), it is clear that none of the sample means are within 1 inch of the population mean.

P渭-1鈮�x鈮�渭+1=P(78.6-1鈮�x鈮�78.6+1)=P(77.6鈮�x鈮�79.6)=11=1

On interpreting, we can say that there is 100%change that the mean height of the four players selected will be within 1 inch of the population mean.

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Most popular questions from this chapter

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.

Explain why increasing the sample size tends to result in a smaller sampling error when a sample means is used to estimate a population mean.

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.

7.67 Brain Weights. In 1905, R. Pearl published the article "Biometrical Studies on Man. 1. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of S wedish men are normally distributed with a mean of 1.40kg and a standard deviation of 0.11kg

a. Determine the sampling distribution of the sample mean for samples of size 3 Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three Swedish men.

b. Repeat part (a) for samples of size 12

c. Construct graphs similar to those shown in Fig. 7.4on page 304 .

d. Determine the percentage of all samples of three Swedish men that have mean brain weights within 0.1kg of the population mean brain weight of 1.40kg. Interpret your answer in terms of sampling error.

e. Repeat part (d) for samples of size 12

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?
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