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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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A variable of a population has mean μ and standard deviation. that For a large sample size n, answer the following questions.
a. Identify the distribution of
b. Does your answer to part (a) depend on n being large? Explain your answer.
c. Identify the mean and the standard deviation of
d. Does your answer to part (c) depend on the sample size being large? Why or why not?
Refer to Exercise 7.6 on page 295.
a. Use your answers from Exercise 7.6(b) to determine the mean, , of the variable for each of the possible sample sizes.
b. For each of the possible sample sizes, determine the mean, , of the variable , using only your answer from Exercise 7.6(a).
7.43 NBA Champs. Repeat parts (b) and (c) of Exercise 7.41 for samples of size 3. For part (b), use your answer to Exercise 7.13(b).
Early-Onset Dementia. Dementia is the loss of intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing Evidence-Based Guidelines for Practice" (Al=hcimer's Care Quarterly, Vol. 5, Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. If the mean age at diagnosis of all people with early-onset dementia is 55 years, find the probability that a random sample of such people will have a mean age at diagnosis less than years. Assume that the population standard deviation is years. State any assumptions that you are making in solving this problem.
Each years, Forbers magazine publishes a list of the richest people in the United States. As of September 16, 2013,the six richest Americans and their wealth (to the nearest billion dollars) are as shown in the following table. Consider these six people a population of interest.
Part (a): Calculate the mean wealth, , of the six people.
Part (b): For samples of size 2, construct a table similar to Table 7.2 on page 293. (There are 15 possible samples of size 2.)
Part (c): Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.
Part (d): For a random sample of size2, what is the chance that the sample mean will equal the population mean?
Part (e): For a random sample of size 2, determine the probability that the mean wealth of the two people obtained will be within 3 of the population mean. Interpret your result in terms of percentages.
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