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Chapter 7: Q. 7.44 (page 301)

NBA Champs Repeat parts (b) and (c) of Exercise 7.41 for samples of size 4. For part (b), use your answer to Exercise 7.14(b).

Short Answer

Expert verified

For the samples of size 4, the mean of the variablex炉is 渭x炉=78.6.

Step by step solution

01

Step 1. Given Information

We have to determine the sample mean for exercise 7.41 for samples of size 4. The given sample in exercise 7.41 as:

02

Step 2. Find the sample mean

In the table below, the samples of size 4 and their respective means are obtained:

SampleHeightMean Height (x炉)
B,W,J,C83,76,80,74
83+76+80+744=78.25
B,W,J,H83,76,80,80
83+76+80+804=79.75
B,W,C,H83,76,74,80
83+76+74+804=78.25
B,J,C,H83,80,74,8083+80+74+804=79.25
W,J,C,H76,80,74,8076+80+74+804=77.5

The variable x炉has the following mean

role="math" localid="1652632975136" 渭x炉=78.25+79.75+78.25+79.25+77.55渭x炉=3935渭x炉=78.6

So when the sample size is 4, the variable x炉has a mean 渭x炉=78.6.

03

Step 3. Find the sample mean using the population mean

We know that mean of the sample mean is equal to the population mean irrespective of the sample size.

Here, for the given data the population mean is 渭=78.6.

So the mean of the sample mean of sample size 4 is

渭x炉=渭=78.6

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Most popular questions from this chapter

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.

According to The Earth: Structure, Composition and Evolution for earthquakes with a magnitude of 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 437 days and a standard deviation of 399 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of7.5 or greater on Richter scale.

Part (a): On average, what would you expect to be the mean of the four times?

Part (b): How much variation would you expect from your answer in part (a)?

Why is obtaining the mean and standard deviation ofxa first step in approximating the sample distribution of the sample mean by a normal distribution.

Population data: 3,4,7,8

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.

Relative to the population mean, what happens to the possible sample means for samples of the same size as the sample size increases? Explain the relevance of this property in estimating a population means by a sample mean.
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