12) the Mean Top of Knee Height of a Sitting Male Is 20
12) The mean top of knee height of a sitting male is 20.7in.
H0: =20.7, H1:
15) Plain M&M candies have a mean weight that is a least 0.8535g.
H0: <20.7, H1:
16) The percentage of workers who got a job through their college is no more than 2%
H0: p>0.02, H1:
19) Right-tailed test;a=0.01
Critical value=2.33
20) Left-tailed test;a=0.05
Critical value=-1.645
12) Travel Through the Internal.Among 734 randomly selected internel users,it was found that 360 of them use the internet for making travel plans(based on data from a Gallup poll).Use a 0.01 significance level to test the claim that among internet users,less than 50% use it for making travel plans.Are the results important for travel agents?
H0: H1:
z-statistics=(360/734-0.5)/sqrt((360/734)*(374/734)/734)=-0.52
critical value=-z(0.01)=-2.33
since z- statistics>-2.33, we can not reject H0.
Conclusion: among internet users, at least 50% use it for making travel plans.
It is very important to travel agent, with many people using internet to make travel plan, the travel agent should improve their website to attract more customer.
13) Percentage of E-mail users.Technolongy is dramatically changing the way we communicate.In 1997,a survey of 880 U.S. households showed that 149 of them use e-mail(based on data from The World Almanac and Book of Facts).Use those sample results to test the claim that 15% of U.S. households use e-mail. Use a 0.05 significance level.Is the conclusion vaild today?Why or why not
H0: H1:
z-statistics=(149/880-0.15)/sqrt((149/880)*( 731/880)/880)=1.53
critical value=z(0.025)=1.96
since z- statistics<1.96, we can not reject H0.
Conclusion: there is 15% of U.S. households use e-mail in 1997.
I do not think the conclusion is valid today since people who use emails increase by a lot in the past few years.
13) Perception of time.Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 min(or 60sec) has passed.Forty students yielded a sample mean of 58.3 sec.Assuming that a=9.5 sec,use a 0.05 significance level to test the claim that the population mean is equal to 60 sec.Based on the result ,does there appear to be an overall perception of 1 min that is reasonably accurate?
H0: H1:
t-statistics=(58.3-60)/9.5*sqrt(40)=-1.13
critical value=t(0.025,39)=2.02
since -2.02<t- statistics<2.02, we can not reject H0.
Conclusion population mean is equal to 60 sec.
17)Blood Pressure Levels.When 14 different second-year medical students at bellevue hospital measured the systolic blood pressure of the same person,they obtained the results listed below(in mmHg).Assuming that the population standard deviation is known to be 10 mmHg,use a significance level to test the claim that the mean blood perssure level that is too high because it is 140 mmHg or greater.Based on the hypothesis test results,can it be safely concluded that the person does not have hypertension?
138,130,135,140,120,125,120,130,130,144,143,140,130,150
Sample mean=133.93
H0: H1:
z-statistics=(133.93-140)/10*sqrt(14)=-2.27
critical value=z(0.05)=1.645
since z- statistics<1.645, we can not reject H0.
Conclusion the mean blood perssure level that is not too high at 0.05 level. We cannot safely conclude that the person does not have hypertension.
19)Appendix B Data set: Weights of Quarters. Use the weights of the post-1964 quarters listed in data set 14 from appendix B.Assuming that quarters are minted to produce with 0.01 significance level to test the claim that the quarters are from a population with mean of 5.670g.Do the quarters appear to be manufactured according to the U.S. mint specification that mean is equal to 5.670g.?
No data!
11) Hypothesis Test for Magnet Treatment of Pain.Researchers conducted a study to determine whether magnets are effective in treating back pain,with results given below( based on data from Biopolar premanent magnets for the treatment of Chronic Lower Back Pain:A pilot study" by Collacott,Zimmerman,White and Rindone.Journal of the American Medical Assocation,Vol.283.No.10). The values repersent measurements of pain using the visual analog scale.Use a 0.05 significance level to test the claim that those given a sham treatment(similar to a placebo)have pain reductions that vary more than the pain reductions for those treated with magnets.
Reduction in pain level after sham treatment:n=20,x=0.44,s=1.4
Reduction in pain level after magnet treatment: n=20,x=0.49,s=0.96
H0: H1:
F-statistics=1.4^2/0.96^2=2.13
critical value=F(0.05,19,19)=2.17
since F- statistics<2.17, we can not reject H0.
Conclusion those given a sham treatment do not have pain reductions that vary more than the pain reductions for those treated with magnets.
15) Weights of Quarters.Weights of quarters are used by vending machines as one way to detect counterfeit coins.Data set 14 in Appendix B includes weights of pre-1964 silver quarters and post-1964 quarters.Here are the summary statistics:pre-1964:n=40,x=6.19267g,s=0.08700g:post1964:n=40,x=5.63930g,s=0.06194.Use a 0.05 significance level to test the claim that the two population of quarters have the same standard deviation.If the amounts of variation are different,vending machines might need more complicated adjustments.Does it appear that such adjustments are necessary?
H0: H1:
F-statistics=0.087^2/0.06194^2=1.97
critical value=F(0.05,39,39)=1.71
since F- statistics>1.71, we can reject H0.
Conclusion: standard deviation are different. Machines need more adjustments
Sect 10-2.Testing for linear Correlation. In exercises 17,21,23.construction a scatterpolt,find the vaule of the linear correlation coefficient r,find the critical value of r from table a-6 by using a=0.05,and determine whether there is a linear correlation between the two variables.Save your work because the same data sets will be used in section 10-3 exercises.
17) Bear Chest Size and Weight.Listed below are the chest sizes(in inches) and weights(in pounds) of randomly selected bears that were anesthetized and measured(based on data from Gary Alt and Minitab,Inc).Because it is much more difficult to weigt a bear than measure its chest size,the presence of a correlation could lead to a method for estimating weight based on chest size.Is there a linear correlation between chest size and weight?
Chest Size | 26 45 54 49 35 41 41 49 38 31
Weight | 80 344 416 348 166 220 262 360 204 144
r=0.98
critical value=0.632
since 0.98>0.632, we conclude that there is a linear correlation.
21) Buying a TV Audience.The new york post published the annual salaries(in millions) and the number of viewers(in millions),with results given below for Oprah Winfrey,David Letterman,Jay Leno,Kelsey Grammer,Barbara Walters,Dan Rather,James Gandolfini,and Susan Lucci,repsectively.Is there a correlation between salary and number of viewers? Which of the listed stars has the lowest cost per viewer?Highest cost per viewer?
Salary | 100 14 14 35.2 12 7 5 1
Viewers | 7 4.4 5.9 1.6 10.4 9.6 8.9 4.2
r=0.12
critical value=0.707
since 0.12<0.707, we can not reject H0.
Conclusion: there is no linear correlation between salary and number of viewers.
Susan Lucci has the lowest cost per viewer.
Kelsey Grammer has the highest cost per viewer.
23) Temperatures and Marathons.In"The Effects of Temperature on marathon runner's Performance"By david Martin and John Buoncristiani(Chance,Vol 12,No 4),high temperatures and times (in minutes)were given for women who won the New York City marathon in recent years.Results are listed below.Is there a correlation between temperature and winning time?Does it appear that winning times are affected by temperatures?
x(temperatures) | 55 61 49 62 70 73 51 57
y(time) | 145.283, 148.717, 148.300, 148.100, 147.617, 146.400 , 144.667, 147.533
r=0.18
critical value=0.707
since 0.18<0.707, we can not reject H0.
Conclusion: there is no linear correlation between temperatures and time.
it appear that winning times are not affected by temperatures
Sect 10-3.Finding the Equation of the Regreesion Line and Making Predictions.Exercises 17,21,23. use the same data sets as exercises 17,21,23 in section 10-2.In each case,find the regression equation,letting the first variable be the independent (x) variable.Find the indicated predicted values.Caution: When finding predicted values,be sure to follow the prediction procedure described in the section.
17) Bear Chest Size and Weight.Find the best predicted weight ( in pounds) of a bear with a chest size of 50 in.
Chest size| 26 45 54 49 35 41 41 49 38 31
Weight | 80 344 416 348 166 220 262 360 204 144
Y=12.38x-251.95
When x=50, y=367.05
21) Buying a Tv audience.Find the best predicted number of viewers for a television star with a salary of $2 million.(In the table below ,the salaries are in millions of dollars and the numbers of viewers are in millions.)
Salary | 100 14 14 35.2 12 7 5 1
Viewers | 7 4.4 5.9 1.6 10.4 9.6 8.9 4.2
Y=-0.011x+6.76
When x=2, y=6.74
23) Temeperatures and Marathons.Find the best predicted winning time for the 1990 marathons when the temeperatures was 73 drgrees.How does that predicted winning time compare to the actual winnning time of 150.750min?
x(temeperatures)| 55 61 49 62 70 73 51 57
y(time) |145.283,148.717,148.300,148.100,147.617,146.400,144.667,147.533
Y=0.032x+145.19
When x=73, y=147.53
When y=150.75, x=173
11) Deaths from Car Crashes.Randomly selected deaths from car crashes were obtained and the results are included in the table below(based on data from the insurance institute for highway safety).Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency on the different days of the week.How might the results be explained?Why does there appear to be an exeeptionally large number of car crash fatalities on saturday?
Day |Sun mon tues wed thurs fri sat
Number of fatalities|132 98 95 98 105 133 158
Chi-square statistics=(132-117)^2/117+(98-117)^2/117+(95-117)^2/117+(98-117)^2/117+(105-117)^2/117+(133-117)^2/117+(158-117)^2/117=30
Critical value=chi-square(0.05,6)=12.6
Since Chi-square statistics> Critical value, we reject the conjecture that car crash fatalities occur with equal frequency on the different days of the week. We see that there are many crash on Friday, Saturday and Sunday because many people drive on these days.
21) M&M Candies.Mars.Inc,claims that its M&M plain candies are distributed with the following color percentages: 16% green ,20%orange ,14% yellow , 24% blue , 13% red , and 13% brown.Refer to data set 13 in appendix B and use the sample data to test the claim that the color distribution is as claimed by Mars.Inc.Use a 0.05 significance level.
No Data.
11) Accuracy of Polygraph Tests.The data in the accompanying table summarize results from tests of the accuracy of polygraphs(based on data from the Office of Technology Assessment).Use a 0.05 signficance level to test the claim that whether the subject lies is independent of the polygraph indication.What do the results suggest about the effectiveness of polygraphs?
Polygraph indicated truth Polygraph indicated lie
Subject actually told the truth | 65 15
Subject actually told a lie | 3 17
Chi-square statistics=(65-54.4)^2/54.4+(15-25.6)^2/25.6+(3-13.6)^2/13.6+(17-6.4)^2/6.4=32.27
Chi-square critical value=chi-square(0.05,1)=3.84
Since Chi-square statistics>critical value, we reject subject lies is independent. Polygraph is good to detect subject who actually tell a lie, but not good to detect subject who actually tell a truth.
17) Occupational Hazards. Use the data in the table to test the claim that occupational is independent of whether the casue of death was homcide .The table is based on data from the U.S. department of labor,bureau of labor statistics.Does any particular occupation appear to be most prone to homicides?If so ,which one?
Police Cashiers Taxi Drivers Guards
Homicide | 82 107 70 59
not homicide | 92 9 29 42
Chi-square statistics=65.52
Chi-square critical value=chi-square(0.05,3)=7.82
Since Chi-square statistics>critical value, we reject occupational is independent. Police and Cashiers appear to be most prone to homicides.
Sect 12-2 In exercise 11.use the listed sample data from car crash experiments conducted by the national transportation safety administration.New cars were purchased and crashed into a fixed barrier at 35mi/h,and the listed measurements were recorded for the dummy in the driver's seat.The subcompact cars are the Ford Escord , Honda Civic , Hyundai Accent , Nissan Sentra,and Saturn SL4.The compact cars are Chevrolet Cavalier , Dodge Neon , Mazad 626 DX ,Pontiac Sunfire , and Subaru Legacy.The midsize cars are Chevrolet Camaro , Dodge Intrepid ,Ford Mustang , Honda Accord , and Volvo S70. The full size cars are Audi A8, Cadillac Deville, Ford Crown Victoria, Oldsmoblie Aurora, and Pontiac Bonneville.
11) Head injury in a car crash.The head injury data(in hic) are given below.Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean.Do the data suggest that larger cars are safer?
Subcompact: 681 428 917 898 420
Compact: 643 655 442 514 525
Midsize: 469 727 525 454 259
Full size: 384 656 602 687 360
Sicne F-statistics<critical value, we cannot reject the conjecture that the different weight categories have the same mean. The data do not suggest that larger cars are safer.