Mathematical Statistics with Applications
7th Edition
ISBN: 9781133384380
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
Publisher: Cengage Learning US
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Chapter 11.5, Problem 30E
a.
To determine
Conduct a test of hypotheses that the slopes are significantly different from zero with two cases.
b.
To determine
Conduct a hypothesis test that two types of catalyst produce the same slope.
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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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- Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=8.2052+0.5693?Y^=8.2052+0.5693X What is the value of ?ˆY^ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. ?ˆ= Interpret the value of ?ˆ. The value of ?ˆ is the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the probability that a crab will be 21.7865 months old. the predicted size of a crab when it is 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months.arrow_forwardUse the least squares regression line of this data set to predict a value. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The least squares regression line of this data set is: y = 8.116x + 273.273 How much rainfall does this line predict in a year if the average temperature of coastal waters is 15 degrees Celsius? Round your answer to the nearest integer. millimetresarrow_forwardThe least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.arrow_forward
- The presence of the sea lice, a common parasite among saltwater fish is said to be related to pollution in the bodies of water. A total of 50 random sample of fish from a certain bay was obtained. Each fish was analyzed whether an internal parasite (Y=1) was observed or not. Likewise, the amount of estrogenic compounds in the fish blood (X₁, ppt) and the sex of the fish (X₂, Male=1 and Female=0), using Female as base category, were recorded. Regression analysis was done, and the model is given by: = -1.3 +0.34X₁ + 1.51X₂ 1. 2. 3. In (y=1) 1-z(y=1) Based on the model, what is the odds of observing an internal parasite over not observing for male relative to a female fish, holding amount of estrogenic compounds constant. A Lower by 1.51 B. Higher by 1.51 C. Lower by e^1.51 D. Higher by e^1.51 Based on the model (holding sex of the fish constant), every ppt increase in the amount of estrogenic compound A. Increases B. decreases the odds of observing an internal parasite multiplicatively…arrow_forwardIn the regression modelY = β0 + β1X1 + β2X2 + εthe extent of any multi collinearity can be evaluated by finding the correlation between X1 and X2 in the sample. Explain why this is so.arrow_forwardExplain why Y is considered the least squares estimator of the mean of Y, µy.arrow_forward
- The presence of the sea lice, a common parasite among saltwater fish are said to be related to pollution in the bodies of water. A total of 50 random sample of fish from a certain bay was obtained. Each fish was analyzed whether an internal parasite (Y=1) was observed or not. Likewise, the amount of estrogenic compounds in the fish blood (X₁, ppt) and the sex of the fish (X₂, Male=1 and Female=0), using Female as base category, were recorded. Regression analysis was done, and the model is given by: -1.3 +0.34X₁ + 1.51X₂ Outcome In 0 (with parasite) 1 (without parasite) (y=1) 1-x(y=1) A researcher wants to validate the model above. He observed 30 random sample of fish from the same bay. He came up with a confusion matrixbelow. Predicted Probability = 0.5 2 25 2. The appropriate test procedure to assess the overall fit of the model is A. Bartlett's test B. Levene's test C. Wald's W test D. t-test 3. Suppose in his test for the overall assessment of the model outputs a p-value of 0.0001,…arrow_forwardA regression was run to determine if there is a relationship between the happiness index (y) and lifeexpectancy in years of a given country (x). The results of the regression were: y^=a+bx ; a=-0.423 ,b=0.07 a. Write the equation of the Least Squares Regression line.b. Find the value for the correlation coefficient, r?c. If a country increases its life expectancy, the happiness index will Increase or decrease ( circleone)d. If the life expectancy is increased by 1 year in a certain country, how much will the happinessindex change? Round to two decimal places.e. Use the regression line to predict the happiness index of a country with a life expectancy of 85years. Round to two decimal places.-arrow_forwardSuppose that a random sample of 194 twenty-year-old men is selected from a population and that their heights and weights are recorded. A regression of weight on height yields Weight = (-96.4277)+ 3.8218 × Height, R² = 0.786, SER = 9.8940 (2.0855) (0.3007) where Weight is measured in pounds and Height is measured in inches. A man has a late growth spurt and grows 1.4550 inches over the course of a year. Construct a confidence interval of 95% for the person's weight gain. The 95% confidence interval for the person's weight gain is (,) (in pounds). (Round your responses to two decimal places.)arrow_forward
- X” denote the number of children ever born to a woman, and let “Y” denote years ofeducation for the woman. A simple model relating fertility to years of education is X = β0 + β1Y + u where u is the unobserved error. (i) What kind of factors are contained in u? Are these likely to be correlated with level of education?arrow_forwardA study was done to investigate the relationship between amount of protix (a new protein-vitamin•-mineral supplement) org a fortified- vitamin rice, known as FVR, and the gain in weight of children. Ten randomly chosen sections of grade one pupils were fed with FVR containing protix; different amounts X of protix were used for the 10 sections. The increase in the weight of each child was measured after a given period. The average gain Y in weight for each section with a prescribed protix level x is as follows; Section(i) Protix(X) Gain(Y) Section(i) Protix(X) Gain(Y) 1 2 3 4 5 50 60 70 80 90 91.6 96.5 95.5 101.3 104.8 6 7 8 9 10 100 110 120 130 140 105.2 107.9 107.4 109.2 109.8 Compute the prediction equation to predict the gain in the weight of a child.arrow_forwardI ONLY NEED PART C,D, and E answered please thanks A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.102b=0.074 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -0.858 -1.07 1.07 0.858 (c) If a country increases its life expectancy, the happiness index will decrease increase (d) If the life expectancy is increased by 2.5 years in a certain country, how much will the happiness index change? Round to two decimal places._____(e) Use the regression line to predict the happiness index of a country with a life expectancy of 63 years. Round to two decimal places._______Use the space below to type your answer AND/OR to upload a picture of your work for all the questions in this problem.arrow_forward
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