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Chapter 7: Q.7.26 (page 300)
Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it ?
The sampling distribution of a sample is frequently approximated by the Normal Distribution.
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Nurses and Hospital Stays. In the article "A Multifactorial Intervention Program Reduces the Duration of Delirium. Length of Hospitalization, and Mortality in Delirious Patients (Journal of the American Geriatrics Society, Vol. 53. No. 4. pp. 622-628), M. Lundstrom et al. investigated whether education programs for nurses improve the outcomes for their older patients. The standard deviation of the lengths of hospital stay on the intervention ward is days.
a. For the variable "length of hospital stay," determine the sampling distribution of the sample mean for samples of patients on the intervention ward.
b. The distribution of the length of hospital stay is right-skewed. Does this invalidate your result in part (a)? Explain your answer.
c. Obtain the probability that the sampling error made in estimating the population means length of stay on the intervention ward by the mean length of stay of a sample of patients will be at most days.
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?
7.45 NBA Champs. Repeat parts (b) and (c) of Exercise for samples of size . For part (b). use your answer to Exercise .
Why is obtaining the mean and standard deviation of a first step in approximating the sample distribution of the sample mean by a normal distribution?
A variable of a population has a mean of and a standard deviation of
a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size
b. Can you answer part (a) if the distribution of the variable under consideration is unknown? Explain your answer.
c. Can you answer part (a) if the distribution of the variable under consideration is unknown but the sample size is instead of ?
Why or why not?
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