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 11.5, Problem 27E
Use the properties of the least-squares estimators given in Section 11.4 to complete the following.
a Show that under the null hypothesis H0 : βi = βi0
possesses a t distribution with n − 2 df, where i = 1, 2.
b Derive the confidence intervals for βi given in this section.
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2. We performed a linear regression using 25 observations. From the regression output we find that bo = 5.7, bị = 12.9, x = 11.4,
Sz = 3.2 and MSE = 12.25.
a. From the least squares line, what is the predicted response when x* = 10.65?
y =
b. What is the 95% confidence interval for the mean response when x* = 10.65?
c. What is the 95% prediction interval for an individual response when x* = 10.65?
d. Which interval is wider? The confidence interval or the prediction interval?
O a. Confidence Interval
b. Prediction Interval
A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n = 10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all. The dependent variable is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. (Hint: start with the df column).
Source
SS
df
MS
Between
___
___
15
F = 7.50
Within
___
___
___
Total
___
___
A least-squares regression line for a set of data with dependent variable y and independent variable x produces a 95% confidence interval [-0.5,1.8]
on the regression slope (beta). We can conclude that:
the predicted value of y for a given x will lie in the range [-0.5x,1.8x] 95% of the time
the regression slope must be zero
O beta will fall inside the range [-0.5,1.8] 95% of the time
The data show no evidence of a linear relation between x and y
O none of these
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. 2ECh. 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. 5ECh. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7ECh. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9ECh. 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. 17ECh. 11.4 - Prob. 18ECh. 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. 22ECh. 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. 30ECh. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36ECh. 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. 41ECh. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 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. 49ECh. 11.8 - Prob. 50ECh. 11.8 - Prob. 51ECh. 11.8 - Prob. 52ECh. 11.8 - Prob. 54ECh. 11.8 - Prob. 55ECh. 11.8 - Prob. 57ECh. 11.8 - Prob. 58ECh. 11.8 - Prob. 59ECh. 11.8 - Prob. 60ECh. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62ECh. 11.9 - Prob. 63ECh. 11.9 - Prob. 64ECh. 11.9 - Prob. 65ECh. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67ECh. 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. 72ECh. 11.12 - Prob. 73ECh. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75ECh. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77ECh. 11.13 - Prob. 78ECh. 11.13 - Prob. 79ECh. 11.14 - Prob. 80ECh. 11.14 - Prob. 81ECh. 11.14 - Prob. 82ECh. 11.14 - Prob. 83ECh. 11.14 - Prob. 84ECh. 11.14 - Prob. 85ECh. 11.14 - Prob. 86ECh. 11.14 - Prob. 87ECh. 11.14 - Prob. 88ECh. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90ECh. 11.14 - Prob. 91ECh. 11.14 - Prob. 92ECh. 11.14 - Prob. 93ECh. 11.14 - Prob. 94ECh. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SECh. 11 - Prob. 98SECh. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 102SECh. 11 - Prob. 103SECh. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SECh. 11 - Prob. 106SECh. 11 - Prob. 107SE
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- A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=10n=10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 6.68 Within 4.35 TOTAL Use the =FDIST() function in Excel to locate the p-value for this ANOVA:p-value = Report p-value accurate to at least 6 decimal places.If you use a significance level of α=.05α=.05, what would you conclude about these treatments?arrow_forwardA pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=9n=9 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 4.07 Within 2.71 TOTAL Use the =FDIST() function in Excel to locate the p-value for this ANOVA:p-value = Report answer accurate to at least 4 decimal places.arrow_forwardA pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=8n=8 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 4.53 Within 4.18 TOTAL Use the =FDIST() function in Excel to locate the p-value for this ANOVA:p-value = Report answer accurate to at least 4 decimal places.If you use a significance level of α=.05α=.05, what would you conclude about these treatments? These data do not provide evidence of a difference between the treatments There is a significant…arrow_forward
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