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 11.7, Problem 46E

Refer to Exercise 11.16. Find a 95% prediction interval for the potency of a 1-ounce portion of antibiotic stored at 65◦F. Compare this interval to that calculated in Exercise 11.39.

11.16 An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of the following Fahrenheit temperatures: 30◦, 50◦, 70◦, and 90◦. The potency readings observed at the end of the experimental period were as shown in the following table.

Chapter 11.7, Problem 46E, Refer to Exercise 11.16. Find a 95% prediction interval for the potency of a 1-ounce portion of

a Find the least-squares line appropriate for this data.
b Plot the points and graph the line as a check on your calculations.
c Calculate S².

11.39 Refer to Exercise 11.16. Find a 95% confidence interval for the mean potency of a 1-ounce portion of antibiotic stored at 65◦F.

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 11.7, Problem 45E

Chapter 11.7, Problem 47E

Chapter 11 Solutions

Mathematical Statistics with Applications

Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2E Ch. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5E Ch. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7E Ch. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9E Ch. 11.3 - Suppose that we have postulated the model...

Ch. 11.3 - Some data obtained by C.E. Marcellari on the...Ch. 11.3 - Processors usually preserve cucumbers by...Ch. 11.3 - J. H. Matis and T. E. Wehrly report the following...Ch. 11.4 - a Derive the following identity:...Ch. 11.4 - An experiment was conducted to observe the effect...Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - A study was conducted to determine the effects of...Ch. 11.4 - Suppose that Y1, Y2,,Yn are independent normal...Ch. 11.4 - Under the assumptions of Exercise 11.20, find...Ch. 11.4 - Prob. 22E Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Do the data in Exercise 11.19 present sufficient...Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Let Y1, Y2, . . . , Yn be as given in Exercise...Ch. 11.5 - Prob. 30E Ch. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32E Ch. 11.5 - Prob. 33E Ch. 11.5 - Prob. 34E Ch. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36E Ch. 11.6 - Using the model fit to the data of Exercise 11.8,...Ch. 11.6 - Refer to Exercise 11.3. Find a 90% confidence...Ch. 11.6 - Refer to Exercise 11.16. Find a 95% confidence...Ch. 11.6 - Refer to Exercise 11.14. Find a 90% confidence...Ch. 11.6 - Prob. 41E Ch. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43E Ch. 11.7 - Prob. 44E Ch. 11.7 - Prob. 45E Ch. 11.7 - Refer to Exercise 11.16. Find a 95% prediction...Ch. 11.7 - Refer to Exercise 11.14. Find a 95% prediction...Ch. 11.8 - The accompanying table gives the peak power load...Ch. 11.8 - Prob. 49E Ch. 11.8 - Prob. 50E Ch. 11.8 - Prob. 51E Ch. 11.8 - Prob. 52E Ch. 11.8 - Prob. 54E Ch. 11.8 - Prob. 55E Ch. 11.8 - Prob. 57E Ch. 11.8 - Prob. 58E Ch. 11.8 - Prob. 59E Ch. 11.8 - Prob. 60E Ch. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62E Ch. 11.9 - Prob. 63E Ch. 11.9 - Prob. 64E Ch. 11.9 - Prob. 65E Ch. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67E Ch. 11.10 - Fit the quadratic model Y=0+1x+2x2+ to the data...Ch. 11.10 - The manufacturer of Lexus automobiles has steadily...Ch. 11.10 - a Calculate SSE and S2 for Exercise 11.4. Use the...Ch. 11.12 - Consider the general linear model...Ch. 11.12 - Prob. 72E Ch. 11.12 - Prob. 73E Ch. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75E Ch. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77E Ch. 11.13 - Prob. 78E Ch. 11.13 - Prob. 79E Ch. 11.14 - Prob. 80E Ch. 11.14 - Prob. 81E Ch. 11.14 - Prob. 82E Ch. 11.14 - Prob. 83E Ch. 11.14 - Prob. 84E Ch. 11.14 - Prob. 85E Ch. 11.14 - Prob. 86E Ch. 11.14 - Prob. 87E Ch. 11.14 - Prob. 88E Ch. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90E Ch. 11.14 - Prob. 91E Ch. 11.14 - Prob. 92E Ch. 11.14 - Prob. 93E Ch. 11.14 - Prob. 94E Ch. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SE Ch. 11 - Prob. 98SE Ch. 11 - Prob. 99SE Ch. 11 - Prob. 100SE Ch. 11 - Prob. 102SE Ch. 11 - Prob. 103SE Ch. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SE Ch. 11 - Prob. 106SE Ch. 11 - Prob. 107SE

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