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Chapter 6: Q4 (page 263)

Sampling Distribution Data Set 4 鈥淏irths鈥� in Appendix B includes a sample of birth weights. If we explore this sample of 400 birth weights by constructing a histogram and finding the mean and standard deviation, do those results describe the sampling distribution of the mean? Why or why not?

Short Answer

Expert verified

No, the results based on one sample of 400 births will not represent the sampling distribution of the sample mean birth weight because to infer about the distribution of the sample mean, all the possible samples of a fixed size are required.

Step by step solution

01

Given information

A sample of 400 birth weights is considered. A histogram is plotted for this sample, and, thus, the mean and the standard deviation are computed.

02

Sampling distribution

The sampling distribution of the sample means is obtained by considering all possible samples of the same size from the same population.

The shape of the sampling distribution, the mean value and the standard deviation are computed for the set of samples that are considered.

Here, only one sample of 400 birth weights is selected, and the histogram is plotted for this sample. Further, the mean and the standard deviation of this sample are computed.

Since only one sample is considered, the mean and the standard deviation computed do not describe the sampling distribution of the sample mean.

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Most popular questions from this chapter

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean).

Standard Normal DistributionIn Exercises 17鈥�36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -2.55 and -2.00.

In Exercises 7鈥�10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Median

a. Find the value of the population median.

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table 6-3. (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

c. Find the mean of the sampling distribution of the sample median. d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not?

Critical Values. In Exercises 41鈥�44, find the indicated critical value. Round results to two decimal places.

z0.04

In Exercises 13鈥�20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, theatre seats, and classroom seats. (Hint: Draw a graph in each case.)

Mean

St.Dev.

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

Find the probability that a male has a back-to-knee length between 22.0 in. and 24.0 in.
See all solutions

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