Questions 35 through 41 are based on the following scenario.
In July, 1995, the magazine “Car and Driver” conducted speed tests of five supercars from five different countries: 1 = Japan (Acura NSX-T), 2= Italy (Ferrari F355), 3 = UK (Lotus Esprit S4S), 4 = Germany (Porsche 911 Turbo), 5 = USA (Dodge Viper RT/10). Car and Driver recorded the top speeds (mph) achieved by these cars using as much distance as necessary. Six measurements were made on each car, three in each direction to cancel any grade or wind factors at the test facility. The analysis of variance results for comparing these speed measurements is provided below.
- – – – – O N E W A Y – – – – –
Variable MPH
By Variable CAR car type
Analysis of Variance
Sum of Mean F F
Source D.F. Squares Squares Ratio Prob.
Between Groups 4 1455.1847 363.7962 25.0849 .0000
Within Groups 25 362.5650 14.5026
Total 29 1817.7497
35.What null and alternative hypotheses are being tested by the F-Ratio in the Analysis of Variance table shown above?
36.What assumptions are required for the F-test in the Analysis of Variance table to be valid?
37.At a 5% significance level, what is your decision?
(a)Accept
(b)Reject //<[CDATA[ (function();var a=window.pagespeed;function b()b.prototype.a=function(d,e,c)if(d=document.getElementById(d))if(e=document.getElementById(e))if(c=document.getElementById(c))e.src=d.getAttribute(“src”),c.parentNode.removeChild(c);b.prototype.inlineImg=b.prototype.a;a.b=function()a.dedupInlinedImages=new b;a.dedupInlinedImagesInit=a.b;)(); pagespeed.dedupInlinedImagesInit(); //]]>//<[CDATA[ pagespeed.dedupInlinedImages.inlineImg(‘pagespeed_img_CgjfjIAS_i1′,’pagespeed_img_CgjfjIAS_i2′,’pagespeed_script_3’); //]]>
38.The standard deviation of speeds in each population is represented by ?. Give the estimate of ?.
39.The group sample means (in mph) are: , , , , and . The researchers were interested in examining all 10 pairwise differences. Give the observed test statistic and corresponding p-value based on a t-distribution with 25 degrees of freedom for the difference Porsche–Viper.
40.Fill in the blank. Suppose we want the overall significance level to be at most 0.05. Using the Bonferroni method, the 10 tests should be conducted using a significance level of __.
(a)0.05
(b)0.025
(c)0.0025
(d)0.005
41.Report the effect size for this study, and state approximately how large it is.
Questions 42 through 47 are based on the following scenario.
Three neighbors are having a dispute over whose dog runs the fastest. They decide to do a little experiment. Each dog will run a short distance three times and their times will be recorded. Neighbor Warner knows a little about statistics and decides to use an ANOVA test. The times (in seconds) for the three dogs are listed below.
Jake
11.0
12.9
12.1
Rover
13.5
10.8
14.1
Molly
9.9
13.6
12.8
42.Calculate the sample means for the three dogs. Based on the sample means, which dog do you think is the fastest dog?
43.Besides assuming that the running times of the dogs are normally distributed and that the runs are independent, what else should Neighbor Warner assume?
44.Calculate the MSB. What does this represent?
45.The MSW turns out to be 2.60. What is the value of the test statistic?
46.Based on the test statistic from question 40, what would you tell the 3 neighbors?
47.Construct the individual 95% confidence interval for the mean times of the runs by the dog Jake.