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Chapter 7: Q 3RP. (page 310)
Provide two synonyms for the distribution of all possible sample means for samples of a given size.
1. Sampling distribution of the sample mean.
2. The distribution of the random variable
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What is another name for the standard deviation of the variable ? What is the reason for that name?
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 hours and a standard deviation of hours.
a. For samples of size , 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 .
Women at Work. In the article "Job Mobility and Wage Growth" (Monthly Labor Review. Vol. 128. No. 2, pp. 33-39).
A. Light examined data on employment and answered questions regarding why workers separate from their employers. According to the article, the standard deviation of the length of time that women with one job are employed during the first 8 years of their career is 92 weeks. Length of time employed during the first 8 years of a career is a left-skewed variable. For that variable, do the following tasks.
a. Determine the sampling distribution of the sample mean for simple random samples of 50 women with one job. Explain your reasoning.
b. Obtain the probability that the sampling error made in estimating the mean length of time employed by all women with one job by that of a random sample of 50 such women will be at most 20 weeks.
7.47 Baby Weight. The paper "Are Babies Normal?" by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No, 4. pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is grams ( pounds, ounces) with a standard deviation of 581 grams.
a. Identify the population and variable.
b. For samples of size , find the mean and standard deviation of all possible sample mean weights.
c. Repeat part (b) for samples of size.
In Example 7.5, we used the definition of the standard deviation of a variable to obtain the standard deviation of the heights of the five starting players on a men's basketball team and also the standard deviation of for samples of sizes 1,2,3,4,5.The results are summarized in Table 7.6on page 298. Because the sampling is without replacement from a finite population, Equation (7.1) can also be used to obtain .
Part (a): Apply Equation (7.1) to compute for sample sizes of 1,2,3,4,5. Compare your answers with those in Table 7.6.
Part (b): Use the simpler formula, Equation (7.2) to compute for samples of sizes 1,2,3,4,5.Compare your answers with those in Table 7.6. Why does Equation (7.2)generally yield such poor approximations to the true values?
Part (c): What percentages of the population size are samples of sizes 1,2,3,4,5.
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