Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11.6, Problem 37E
Using the model fit to the data of Exercise 11.8, construct a 95% confidence interval for the
11.8 Laboratory experiments designed to measure LC50 (lethal concentration killing 50% of the test species) values for the effect of certain toxicants on fish are run by two different methods. One method has water continuously flowing through laboratory tanks, and the other method has static water conditions. For purposes of establishing criteria for toxicants, the Environmental Protection Agency (EPA) wants to adjust all results to the flow-through condition. Thus, a model is needed to relate the two types of observations. Observations on toxicants examined under both static and flow-through conditions yielded the data in the accompanying table (measurements in parts per million, ppm). Fit the model
- a What interpretation can you give to the results?
- b Estimate the flow-through value for a toxicant with an LC50 static value of x = 12 ppm.
11.18
- a Calculate SSE and S2 for Exercise 11.8.
- b Refer to Exercise 11.8. Code the x-values in a convenient manner and fit a simple linear model to the LC50 measurements presented there. Compute SSE and compare your answer to the result of part (a).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A researcher developed a regression model to predict the cost of a meal based on the summated rating (sum of ratings for food, decor,and service) and the cost per meal for 12 restaurants. The results of the study show that
b1=1.4379 and Sb1=0.1397.
a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?
b. Construct a 95% confidence interval estimate of the population slope,
β1.
a. Determine the hypotheses for the test. Choose the correct answer below.
A.
H0:
β1=0
H1:
β1≠0
B.
H0:
β0≤0
H1:
β0>0
C.
H0:
β1≤0
H1:
β1>0
D.
H0:
β0≥0
H1:
β0<0
E.
H0:
β1≥0
H1:
β1<0
F.
H0:
β0=0
H1:
β0≠0
Compute the test statistic.
The test statistic is ?
(Round to two decimal places as needed.)
Determine the critical value(s).
The critical value(s) is(are) ?
(Use a comma to separate answers as needed.…
Perform the test hypothesis on the following scenarios.
In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two - tailed with a=0.01 .
In exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4.Click on the datafile logo to reference the data. Use Table 1 of Appendix B.
a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).$
b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).$ to $
c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- In a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that evenmoderate alcohol consumption significantly slowed response time to an emergency situation in a drivingsimulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one6-ounce glass of wine. Again, they used a standardized driving simulation task for which the regular populationaverages μ = 400 msec. The distribution of reaction times is approximately normal with σ = 40. Assume that theresearcher obtained a sample mean of M = 422 for the n = 25 participants in the study.a. Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed testwith α = .01.arrow_forwardIn exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B.Click on the datafile logo to reference the data. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).$ b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).$ to $ c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).$ to $arrow_forwardA regression analysis was conducted to investigate the relationship between the total charge and travel time for a certain car service. Computer output from a linear regression analysis is shown below. The analysis was performed on a sample of 24 observations. Term CoefCoef SE CoefSE Coef Constant −1.55−1.55 0.945 Travel time 0.22 0.023 Assume that the conditions for inference for the slope of the regression equation have been met. Which of the following defines the margin of error of a 90 percent confidence interval for the slope of the least-squares regression line? 1.321(0.945)1.321(0.945) A 1.717(0.945)1.717(0.945) B 1.717(0.22)1.717(0.22) C 1.321(0.023)1.321(0.023) D 1.717(0.023) Earrow_forward
- Perform the test of hypothesis on the following scenarios. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two – tailed with α = 0.01.arrow_forwardAn experiment was conducted to compare the alcohol content of soy sauce on two different production lines. Production was monitored eight times a day. The data are shown here. Production line 1 0.38 0.37 0.39 0.41 0.38 0.39 0.40 0.39 Production line 2 0.48 0.39 0.42 0.52 0.40 0.48 0.52 0.52 Assume both populations are normal. It is suspected that production line 1 is not producing as consistently as production line 2 in terms of alcohol content. Using the 0.05 level of significance, can conclude that the population standard deviations for the alcohol content of these two types of production lines could be the same.arrow_forwardIn Exercises, presume that the assumptions for regression inferences are met.Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise. x 57 85 57 65 52 67 62 80 77 53 68 y 8.0 22.0 10.5 22.5 12.0 11.5 7.5 13.0 16.5 21.0 12.0 a. Obtain a point estimate for the mean quantity of volatile emissions of all (Solanum tuberosum) plants that weigh 60 g.b. Find a 95% confidence interval for the mean quantity of volatile emissions of all plants that weigh 60 g.c. Find the predicted quantity of volatile emissions for a plant that weighs 60 g.d. Determine a 95% prediction interval for the quantity of volatile emissions for a plant that weighs 60 g.ExerciseApplying the Concepts and SkillsIn Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.arrow_forward
- You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=18,you determine that b1=4.6 and Sb1=1.9. c. Based on your answers to (a) and (b), what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, β1.arrow_forwardTo test whether or not there is a significant difference in the average snowfall in Maryland, and Virginia, the average snowfall in the two states during a random sample of 92 days during a leap year were recorded. In Maryland, the average is 5.4 inches with a standard deviation of 0.4 inches and in Virginia, the average is 5.2 inches with a standard deviation of 0.4 inches. Test the hypothesis at a 10% level of significance. Use the F-test to solve the Behrens Fisher problem, use Welsh's approximation, the Wilson Hilferty approximation. Use the p-value method. View keyboard shortcutsarrow_forwardIn a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even moderate alcohol consumption significantly slowed response time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce glass of wine. Again, they used a stan dardized driving simulation task for which the regular population averages μ = 400 msec. The distribution of reaction times is approximately normal with σ = 40. Assume that the researcher obtained a sample mean of M = 422 for the n = 25 participants in the study. a. Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed test with α = .01. b. Do the data provide evidence that the alcohol significantly increased (slowed) reaction time? Use a one-tailed test with α = .01. c. Compute Cohen’s d to estimate the size of the effect.arrow_forward
- The relationship between "strength" and "fineness" of cotton fibers was the subject of a study that produced the following data. (Give your answers correct to two decimal places.) x, Strength 76 69 71 76 83 72 78 74 80 82 y, Fineness 4.5 4.5 4.7 4.2 4.1 4.2 4.8 4.9 4.3 4.5 (a) Find the 98% confidence interval for the mean measurement of fineness for fibers with a strength of 79. Lower Limit Upper Limit (b) Find the 90% prediction interval for an individual measurement of fineness for fibers with a strength of 79. Lower Limit Upper Limitarrow_forwardIn a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even moderate alcohol consumption significantly slowed response time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce glass of wine. Again, they used a standardized driving simulation task for which the regular population averages μ = 400 msec. The distribution of reaction times is approximately normal with σ = 40. Assume that the researcher obtained a sample mean of M = 422 for the n = 25 participants in the study. a. Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed test with α = .01.arrow_forwardIn a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even moderate alcohol consumption significantly slowed response time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce glass of wine. Again, they used a standardized driving simulation task for which the regular population averages μ = 400 msec. The distribution of reaction times is approximately normal with σ = 40. Assume that the researcher obtained a sample mean of M = 422 for the n = 25 participants in the study A) Are the data sufficient to conclude that the alcohol has a significant effect on reaction time? Use a two-tailed test with α = .01. B) Do the data provide evidence that the alcohol significantly increased reaction time? Use a one-tailed test with α = .01 C) Compute Cohen’s d to estimate the size of the effect.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY