4th Edition

ISBN: 9780073401331

Author: William Navidi Prof.

Publisher: McGraw-Hill Education

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Chapter 5.4, Problem 13E

The article “The Prevalence of Daytime Napping and Its Relationship to Nighttime Sleep” (J. Pilcher, K. Michalkowski, and R. Carrigan), Behavioral Medicine, 2001:71–76) presents results of a study of sleep habits in a large number of subjects. In a sample of 87 young adults, the average time per day spent in bed (either awake or asleep) was 7.70 hours, with a standard deviation of 1.02 hours, and the average time spent in bed asleep was 7.06 hours, with a standard deviation of 1.11 hours. The mean time spent in bed awake was estimated to be 7.70 – 7.06 = 0.64 hours. Is it possible to compute a 95% confidence interval for the mean time spent in bed awake? If so, construct the confidence interval. If not possible, explain why not.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 5.4, Problem 12E

Chapter 5.4, Problem 14E

Chapter 5 Solutions

Statistics for Engineers and Scientists

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Solution Summary: The author explains that it is not possible to compute a 95% confidence interval for the mean time spent in bed awake.

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