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Chapter 7: Q.7.27 (page 300)

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

Short Answer

Expert verified

To acquire the exact form of the sampling distribution (normal distant) of the sample mean, we must first obtain the values of the sample mean's mean 渭xand standard deviation蟽x.

Step by step solution

01

Given Information

We have To find The reason is obtaining the mean and standard deviation of xa First step in approximating the sampling distribution of the sample mean by a normal distribution.

02

Explanation

Means 渭and standard deviation 蟽are the parameters of the normal distribution. The values of these parameters 渭&蟽are required to establish the exact form of the normal distortion.

To acquire the exact form of the sampling distribution (normal distant) of the sample mean, we must first obtain the values of the sample mean's mean 渭xand standard deviation 蟽x

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Most popular questions from this chapter

New York City 10-kmRun. As reported by Rum谢械's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9minutes. Do the following for the variable "finishing time61min of finishers in the New York City 10-kmrun.

a. Find the sampling distribution of the sample mean for samples of size 4

b. Repeat part (a) for samples of size 9

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

d. Obtain the percentage of all samples of four finishers that have mean finishing times within 5minutes of the population mean finishing time of 61 minutes. Interpret your answer in terms of sampling error.

e. Repeat part (d) for samples of size 9

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)?

7.50 Undergraduate Binge Drinking. Alcohol consumption on college and university campuses has gained attention because undergraduate students drink significantly more than young adults who are not students. Researchers I. Balodis et al. studied binge drinking in undergraduates in the article "Binge Drinking in Undergraduates: Relationships with Gender, Drinking Behaviors, Impulsivity, and the Perceived Effects of Alcohol" (Behavioural Pharmacology, Vol. 20, No. 5. pp. 518-526). The researchers found that students who are binge drinkers drink many times a month with the span of each outing having a mean of 4.9hours and a standard deviation of 1.1 hours.
a. For samples of size 40, find the mean and standard deviation of all possible sample mean spans of binge drinking episodes. Interpret your results in words.
b. Repeat part (a) with n=120.

A variable of a population is normally distribution with mean 渭and standard deviation 蟽.

a. Identify the distribution of x.

b. Does your answer to part (a) depend on the sample size? Explain your answer.

c. Identify the mean and the standard deviation of x.

d. Does your answer to part (c) depend on the assumption that the variable under consideration is normally distributed? Why or why not?

Refer to Exercise 7.10on page 295.

a. Use your answers from Exercise 7.10(b)to determine the mean, 渭i, of the variable x^for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, 渭i+of the variable x^, using only your answer from Exercise 7.10(a)
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