Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Textbook Question

Chapter 13.7, Problem 22E

a Based on your answers to Exercises 13.20 and 13.21 and the comments at the end of this section, how would you expect confidence intervals computed using the results of this section to compare with related intervals that make use of the data from only one or two of the samples obtained in a one-way layout? Why?

b Refer to part (a). Is it possible that a 95% confidence interval for the mean of a single population based only on the sample taken from that population will be shorter than the 95% confidence interval for the same population mean that would be obtained using the procedure of this section? How?

13.20 Refer to Examples 13.2 and 13.3.

a Use the portion of the data in Table 13.2 that deals only with teaching technique 1 and the method of Section 8.8 to form a 95% confidence interval for the mean score of students taught using technique 1.

b How does the length of the 95% confidence interval that you found in part (a) compare to the length of the 95% confidence interval obtained in Example 13.3?

c What is the major reason that the interval that you found in part (a) is longer than the interval given in Example 13.3?

13.21 Refer to Examples 13.2 and 13.4.

a Use the portion of the data in Table 13.2 that deals only with teaching techniques 1 and 4 and the method of Section 8.8 to form a 95% confidence interval for the difference in mean score for students taught using techniques 1 and 4.

b How does the length of the 95% confidence interval that you found in part (a) compare to the length of the 95% confidence interval obtained in Example 13.4?

c What is the major reason that the interval that you found in part (a) is longer than the interval given in Example 13.4?

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 13.7, Problem 21E

Chapter 13.7, Problem 23E

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Chapter 13 Solutions

Mathematical Statistics with Applications

Ch. 13.2 - The reaction times for two different stimuli in a...Ch. 13.2 - Prob. 2E Ch. 13.4 - State the assumptions underlying the ANOVA of a...Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Suppose that independent samples of sizes n1, n2,,...Ch. 13.4 - Four chemical plants, producing the same products...Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - A clinical psychologist wished to compare three...

Ch. 13.4 - It is believed that women in the postmenopausal...Ch. 13.4 - If vegetables intended for human consumption...Ch. 13.4 - One portion of the research described in a paper...Ch. 13.4 - The Florida Game and Fish Commission desires to...Ch. 13.4 - Prob. 15E Ch. 13.4 - An experiment was conducted to examine the effect...Ch. 13.5 - Prob. 17E Ch. 13.5 - Refer to Exercise 13.17 and consider YiYi for i ...Ch. 13.5 - Refer to the statistical model for the one-way...Ch. 13.7 - Refer to Examples 13.2 and 13.3. a Use the portion...Ch. 13.7 - Refer to Examples 13.2 and 13.4. a Use the portion...Ch. 13.7 - a Based on your answers to Exercises 13.20 and...Ch. 13.7 - Refer to Exercise 13.7. a Construct a 95%...Ch. 13.7 - Prob. 24E Ch. 13.7 - Prob. 25E Ch. 13.7 - Prob. 26E Ch. 13.7 - Prob. 27E Ch. 13.7 - Prob. 28E Ch. 13.7 - Prob. 29E Ch. 13.7 - Prob. 30E Ch. 13.7 - Prob. 31E Ch. 13.7 - Prob. 32E Ch. 13.7 - Prob. 33E Ch. 13.7 - Prob. 34E Ch. 13.7 - Prob. 35E Ch. 13.8 - Prob. 36E Ch. 13.8 - Prob. 37E Ch. 13.8 - Prob. 38E Ch. 13.8 - Prob. 39E Ch. 13.8 - Prob. 40E Ch. 13.9 - Prob. 41E Ch. 13.9 - The accompanying table presents data on yields...Ch. 13.9 - Refer to Exercise 13.42. Why was a randomized...Ch. 13.9 - Prob. 44E Ch. 13.9 - Prob. 45E Ch. 13.9 - Prob. 46E Ch. 13.9 - Prob. 47E Ch. 13.9 - Prob. 48E Ch. 13.9 - Prob. 49E Ch. 13.9 - Prob. 50E Ch. 13.9 - Prob. 51E Ch. 13.10 - Prob. 52E Ch. 13.10 - Prob. 53E Ch. 13.10 - Prob. 54E Ch. 13.10 - Refer to Exercise 13.46. Construct a 95%...Ch. 13.10 - Prob. 56E Ch. 13.10 - Prob. 57E Ch. 13.11 - Prob. 58E Ch. 13.11 - Prob. 59E Ch. 13.11 - Prob. 60E Ch. 13.11 - Prob. 61E Ch. 13.11 - Prob. 62E Ch. 13.12 - Prob. 63E Ch. 13.12 - Prob. 64E Ch. 13.12 - Prob. 65E Ch. 13.12 - Prob. 66E Ch. 13.12 - Prob. 67E Ch. 13.12 - Prob. 68E Ch. 13.13 - Prob. 69E Ch. 13.13 - Prob. 70E Ch. 13.13 - Refer to Exercise 13.42. Answer part (a) by...Ch. 13.13 - Refer to Exercise 13.45. Answer part (b) by...Ch. 13 - Prob. 73SE Ch. 13 - Prob. 74SE Ch. 13 - Prob. 75SE Ch. 13 - Prob. 77SE Ch. 13 - A study was initiated to investigate the effect of...Ch. 13 - Prob. 79SE Ch. 13 - A dealer has in stock three cars (models A, B, and...Ch. 13 - In the hope of attracting more riders, a city...Ch. 13 - Prob. 84SE Ch. 13 - Prob. 85SE Ch. 13 - Prob. 86SE Ch. 13 - Prob. 87SE Ch. 13 - Prob. 88SE Ch. 13 - Prob. 89SE Ch. 13 - Prob. 90SE Ch. 13 - Prob. 92SE Ch. 13 - Prob. 94SE

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