exercise06 - Exercise Questions Chapter 6 6.11 Changing the...

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Exercise Questions: Chapter 6 6.11 Changing the sample size. Suppose that the sample mean is 50 and the standard deviation is assumed to be 5. Make a diagram similar to Figure 6.5 ( page 362 ) that illustrates the effect of sample size on the width of a 95% interval. Use the following sample sizes: 10, 20, 40, and 80. Summarize what the diagram shows. 6.12 Changing the confidence level. A study with 36 observations had a mean of 70. Assume that the standard deviation is 12. Make a diagram similar to Figure 6.6 ( page 363 ) that illustrates the effect of the confidence level on the width of the interval. Use 80%, 90%, 95%, and 99%. Summarize what the diagram shows. 6.17 Mean serum TRAP in young women. For many important processes that occur in the body, direct measurement of characteristics of the process is not possible. In many cases, however, we can measure a biomarker, a biochemical substance that is relatively easy to measure and is associated with the process of interest. Bone turnover is the net effect of two processes: the breaking down of old bone, called resorption, and the building of new bone, called formation. One biochemical measure of bone resorption is tartrate resistant acid phosphatase (TRAP), which can be measured in blood. In a study of bone turnover in young women, serum TRAP was measured in 31 subjects. 7 The units are units per liter (U/l). The mean was 13.2 U/l. Assume that the standard deviation is known to be 6.5 U/l. Give the margin of error and find a 95% confidence interval for the mean for young women represented by this sample. 6.25 Calories consumed by women in the U.S. The mean number of calories consumed by women in the United States who are 19 to 30 years of age is μ = 1791 calories per day. The standard deviation is 31 calories. 9 You will study a sample of 200 women in this age range, and one of the variables you will collect is calories consumed per day. (a) What is the standard deviation of the sample mean (b) The 68–95–99.7 rule says that the probability is about 0.95 that is within ________ calories of the population mean μ . Fill in the blank. (c) About 95% of all samples will capture the true mean of calories consumed per day in the interval plus or minus ________ calories. Fill in the blank. 6.29 Required sample size for specifed margin of error. A new bone study is being planned that will measure the biomarker TRAP described in Exercise 6.17 . Using the value of σ given there, 6.5 U/l, find the sample size required to provide an estimate of the mean TRAP with a margin of error of 2.0 U/l for 95% confidence. ? 6.33 More than one confidence interval. As we prepare to take a sample and compute a 95% confidence interval, we know that the probability that the interval we compute will cover the parameter is 0.95. That’s the meaning of 95% confidence. If we use several such intervals, however, our confidence that all of them give correct results is less than
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