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, Problem 102SE
To determine
State whether the data provide sufficient evidence to support the claim that the mean salary depends on the gender of the faculty members at 0.05 level of significance.
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Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Using the hypothetical data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.
Compact
Midsize
Full-size
643
655
702
680
672
469
427
525
495
483
484
465
402
476
435
State the null and alternate hypothesis for the data.
Given the results, what will be the conclusion of the team?
a. Interpret the effect of a three (3) unit increase in Length on the response of Weight.
b. The p-value to test the null hypothesis that the slope on Length is 0 (H0 : β1 = 0), isapproximately 0. What can you say about Length being a significant explanatory variable orcovariate when explaining Weight?
A researcher recorded the number of e-mails received in a month and the number of online purchases made during that month for 50 people with an online presence. The resulting data were used to conduct a hypothesis test to investigate whether the slope of the population regression line relating number of e-mails received to number of online purchases is positive. What are the correct hypotheses for the test?
H0:β1=0Ha:β1≠0H0:β1=0Ha:β1≠0
A
H0:β1=0Ha:β1>0H0:β1=0Ha:β1>0
B
H0:β1=0Ha:β1<0H0:β1=0Ha:β1<0
C
H0:β1>0Ha:β1=0H0:β1>0Ha:β1=0
D
H0:b1=0Ha:b1≠0
E
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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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardResearchers have shown that cigarette smoking has a deleterious effect on lung function. In their study of the effect of cigarette smoking on the carbon monoxide diffusing capacity (DL) of the lung, Ronald Knudson, W. Kaltenborn and B. Burrows found that current smokers had DL readings significantly lower than either ex-smokers or nonsmokers. The carbon monoxide diffusing capacity for a random sample of current smokers was as follows: 103.768 88.602 73.003 123.086 91.052 92.295 61.675 90.677 84.023 76.014 100.615 88.017 71.210 82.115 89.222 102.754 108.579 73.154 106.755 90.479 Do these data indicate that the mean DL reading for current smokers is lower than 100, the average DL reading for nonsmokers? A. Find the test statistics and interpret the results, a = 0.01? B. Calculate p value and interpret the results. C. Find the confidence interval for a = 0.05.arrow_forwardA large manufacturing company producing air conditioner compressor believes the number of units of air conditioner sold is related to atmospheric temperature. An R&D officer conducted a study and gathered the following data: 3. Day Sale Temperature (Fahrenheit) 63 (in thousands) 1.52 1 2 70 1.68 3 73 1.8 4 75 2.05 80 2.36 6. 82 2.25 7 85 2.68 8 88 2.9 9. 90 3.14 3.06 3.24 10 91 11 92 12 75 1.92 13 98 3.4 14 100 3.28 Construct an estimated regression line between temperature and number of units sold. а) b) Does the model in part (a) confirm that contribution of temperature to number of units of air conditioner sold? Test using a 0.05. Find the coefficient of correlation. What does the value imply about the relationship of the two variables? c) If the temperature soared to 120 Fahrenheit, can you predict the number of units of air conditioner sold? Explain d)arrow_forward
- Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the treatments (cars types). Using the hypothetical data provided below, test whether the mean pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%. Compact cars Midsize cars Full-size cars 643 469 484 655 427 456 702 525 402 Mean 666.67 473.67 447.33 Standard deviation 31.18 49.17 41.68arrow_forwardManagers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of randomly selected days during the past year are given below. These data are plotted in the scatter plot below. (a)For these data, temperature values that are less than the mean of the temperature values tend to be paired with coffee sales values that are ▼(Choose one) the mean of the coffee sales values. (b)According to the regression equation, for an increase of one degree in temperature, there is a corresponding ▼(Choose one) of 9.94 dollars in coffee sales. (c)From the regression equation, what is the predicted coffee sales value (in dollars) when the temperature is 74.6 degrees Fahrenheit? (Round your…arrow_forwardThe following data show the results of random sample of 10 batches of one pattern of product: Support Costs Y Sample Batch Size X 1 15 $120 2 20 130 3 15 200 4 20 250 10 150 6 25 140 7 20 300 8 10 120 15 160 10 30 320 Calculate: Using regression analysis (Y=a+bx ) and predict support cost for a batch size X = $20 then what is Mixed Cost ?arrow_forward
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