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Chapter 7: Q 1RP. (page 310)
Define sampling error?
When an analyst fails to select a sample that accurately represents the entire population of data, a sampling mistake occurs.
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Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it?
7.1 Why is sampling often preferable to conducting a census for the purpose of obtaining information about a population?
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.
Testing for Content Accuracy. A brand of water-softener salt comes in packages marked "net weight ." The company that packages the salt claims that the bags contain an average of of salt and that the standard deviation of the weights is Assume that the weights are normally distributed.
a. Obtain the probability that the weight of one randomly selected bag of water-softener salt will be or less, if the company's claim is true.
b. Determine the probability that the mean weight of 10 randomly selected bags of water-softener salt will be or less, if the company's claim is true.
c. If you bought one bag of water-softener salt and it weighed , would you consider this evidence that the company's claim is incorrect? Explain your answer.
d. If you bought bags of water-softener salt and their mean weight was , would you consider this evidence that the company's claim is incorrect? Explain your answer.
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.
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