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Chapter 6: Q2 (page 272)

Small Sample Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n = 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.

Short Answer

Expert verified

It is incorrect to conclude that the sample means cannot be treated as values from a normal distribution as the sample size is too small because it is mentioned that the population of weights of golden retriever dogs is normally distributed.

Thus, all samples selected from this population will be normally distributed.

Step by step solution

01

Given information

It is given that weights of golden retriever dogs are normally distributed and samples of size equal to 15 are extracted from this population.

02

Requirements under which sample means is said to follow a normal distribution

One of the following requirements must be fulfilled for the computed sample mean to be treated as a value from a normally distributed population.

  • It should be clearly stated that the sample is extracted from the normally distributed population.
  • The sample size should be greater than 30.

Here, it is given that the population of weights of golden retriever dogs is normally distributed. That is, one of the requirements is met.

Thus, the sample means can be treated as being from a normal population as all the samples will be normally distributed.

It is incorrect to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small.

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Most popular questions from this chapter

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, 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 = -3 and z = 3 (or within 3 standard deviation of the mean).

Standard normal distribution, 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 score. If using technology instead of Table A-2, round answers to four decimal places.

Greater than -3.75

Unbiased Estimators Data Set 4 “Births” in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?

In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

In Exercises 7–10, 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 Variance

a. Find the value of the population variance σ2.

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample variance s2. Then combine values of s2that 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 variance.

d. Based on the preceding results, is the sample variance an unbiased estimator of the population variance? Why or why not?
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