One-way ANOVA: MPG versus Car ManufacturerQuiz 2 Name Answer KeyStat 2171. A study was conducted to compare the miles per gallon (MPG) of cars made by 4 different car manufacturers (Ford, Chevy, Dodge, and Honda) that have similar engines and body weight. The MPG measurements were acquired on 6 different cars from each manufacturer. The cars were tested under identical road-track and driver conditions. One-way ANOVA: MPG versus Car ManufacturerAnalysis of Variance for MPG Source DF SS MS F PCar Manuf 3 22.240 7.413 ***** 0.000Error 20 ***** *****Total 23 28.285 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ---+---------+---------+---------+---Ford 6 27.195 0.530 (----*----) Chevy 6 29.146 0.601 (---*----) Dodge 6 27.719 0.377 (---*----) Honda 6 29.511 0.652 (----*----) ---+---------+---------+---------+---Pooled StDev = 0.550 27.0 28.0 29.0 30.0(a) Conduct the overall test (1 pt).- State the appropriate hypotheses. (1 pt)H0: -Ford = -Chevy = -Dodge = -HondaHa: at least one of the means is different- Check the assumption that the population standard deviations are the same (1 pt). Since the largest standard deviation sHonda = .652 is not twice as large as the smallest standard deviation sDodge=.377, then we assume that the standard deviation - for each of the car types are equal.- Give the value of SSE, MSE and the F statistic (2 pts). SSE = SST – SSG = 28.285 - 22.24 = 6.0450MSE = SSE/DFE = 6.0450/20 = .3023F = MSG/MSE = 7.413/.3023 = 24.5261- What is the distribution of the test statistic, assuming that Ho is true? (1 pt) F ~ F(DFG,DFE) = F(2,20)- Give the p-value. (1/2 pt)The p-value is so small that MINITAB estimates it to be practically 0.000- Make a decision. (1/2 pt)A p-value of 0.000 is less than any reasonable significance level (like .01, .02, .05, .1), so we SOUNDLY reject H0. - Make a conclusion in terms of the problem. (1 1/2)There is a landslide of evidence to suggest that the mean mpg of cars differ dependingon whether the car was made by Ford, Chevy Dodge and Honda.Multiple Choice Questions – Circle the one best answer for each question. (1/2 pt each)2. The graph below is a normal quantile plot of the residuals from the ANOVA model on the first page. From this graph, it appears thatA. The residuals are normally distributed.B. The residuals are not normally distributed.C. The residuals are getting larger as the sample size increases10-1210-1-2Normal ScoreResidualNormal Probability Plot of the Residuals(response is MPG)D. None of the above 3. Based on the MINITAB output on the previous page, you might guess that A. The mean mpg for each car manufacturer is different. B. The mean mpg for Ford and Dodge are different than the mean mpg for Chevy and Honda.C. The mean mpg for Honda is higher than all of the others.D. We can not tell from the MINITAB output provided.4. Which of the following is evidence against Ho (and for Ha) in the overall test?A. When the variability among the group means is large compared to the variability within thegroups.B. When the variability among the group means is similar to the variability within the groups.C. When the variability among the group means is small compared to the variability within thegroups.D. When the variability among the group means is equal to the variability within the groups.5. Which of the following is NOT an assumption in one-way ANOVA?A. Independent SRSs are taken from each population.B. The standard deviation is different for each population.C. The residuals are normally distributed for each population.D. None of the above.6. Which of the following is the one-way ANOVA model?A. ijiijxxB. iiijxx C. ijiijxD.