8th Edition

ISBN: 9781337558075

Author: Charles Henry Brase, Corrinne Pellillo Brase

Publisher: Cengage Learning

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter 8.2, Problem 19P

Critical Thinking: Boxplots and Confidence Intervals The distribution of heights of 18-year-old men in the United States is approximately normal. with mean 68 inches and standard deviation 3 inches (U.S. Census Bureau). In Minitab, we can simulate the drawing of random samples of size 20 from this population (► Cale ► Random Data ► Normal, with 20 rows from a distribution with a mean of 68 and a standard deviation of 3). Then we can have Minitab compute a 95% confidence interval and draw a boxplot of the (► Stat ► Basic Statistics ► 1—Sample t, with boxplot selected in the graphs). The boxplots and confidence intervals for four different samples are shown in the accompanying figures. The four confidence intervals are

VARIABLE	N	MEAN	STDEV	SEMEAN	95.0	% CI
Sample 1	20	68.050	2.901	0.649		69.407)
Sample a	20	67.956	3.137	0.702	(66.490	69.426
Sample 3	20	67.976	2.639	0.590	(66.741 ,	69.211)
Sample 4	20	66.908	2.440	0.546	(65.766 ,	68.050)

(a) Examine the figure (parts (a) to (d)). How do the boxplots for the four samples differ? Why should you expect the boxplots to differ ?

Chapter 8.2, Problem 19P, 19 Critical Thinking: Boxplots and Confidence Intervals The distribution of heights of 18-year-old

(b) Examine the 95% confidence intervals for the four sample shown in the printout. Do the intervals differ in length? Do the intervals all contain the expected population mean of tot inches? If we draw more samples, do you expect all of the resulting 95% confidence intervals to contain µ = 68 ? Why or 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 8.2, Problem 18P

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Chapter 8 Solutions

Understanding Basic Statistics

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