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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

Standard Normal Distribution. Find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Doorway Height The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 68.6 in. and a standard deviation of 2.8 in. (based on Data Set 1 鈥淏ody Data鈥� Appendix B).

a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.

b. If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72 in.

c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)?Why?

d. When considering the comfort and safety of passengers, why are women ignored in this case?

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 Standard Deviation For the following, round results to three decimal places.

a. Find the value of the population standard deviation

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviation s. Then combine values of s 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 standard deviation. d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard deviation? Why or why not?

What is the difference between a standard normal distribution and a non-standard normal distribution?

Standard normal distribution. In Exercise 17-36, 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 score. If using technology instead of Table A-2, round answers to four decimal places.

Less than 2.56
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