Question

(1 point) Family transportation costs are usually higher than most people believe. Eighteen randomly selected families in three major cities are asked to use their records to estimate a monthly figure for transportation cost. Use the data obtained and ANOVA to test whether there is a significant difference in monthly transportation costs for families living in these cities. Use a = 0.05. Edmonton 650 480 550 600 675 540 TE Toronto Vancouver 250 850 525 700 950 175 780 500 450 675 300 600 (a) Specify the appropriate statistical hypotheses. O A. Ho : At least one of the means is different from the others HA : The means are the same. OB. Ho : The three population means are the same. HA: At least one of the means is different from the others OC. Ho : The three population means are the same. HA: All three means are different from the others. In order to obtain valid inferences from the one-way ANOVA procedure, check the assumptions need to be reasonably satisfied. (b) Do the data collected from each city follow approximately Normal distribution?(look at the symmetry of boxplots if you cannot run normality tests)? (c) Can the population variances be reasonably assumed to be the same? ? (1) Report your Levene's test of equal variance test statistic value. Use two decimal places. (ii) Report the P-value of your Levene's test of equal variance. Use three decimal places

Answer 1

a). B option is correct.

Null, All means are equal

Alternate - Not all means are equal/atleast one of mean is different.

b).

Yes all the three type of data follows normality.

Below is the minitab output of normality test.

Since for all p-value > 0.05, data follows normal distribution

Probability Plot of Edmonton, Toronto, Vancouver Normal - 95% CI + 7 - Variable Edmonton - Toronto - Vancouver + + + Mean StDev NADP 582.5 73.19 6 0.189 0.822 366.7 144.6 6 0.305 0.443 759.2 1273 6 0.166 0.889 Percent TEHTITE + ++H TNTTTT 4 + + H 0 300 900 1200 600 Data

c). Yes.

i). 2,.52

ii).0.114

Test for Equal Variances: Edmonton, Toronto, Vancouver Method Null hypothesis All variances are equal Alternative hypothesis At least one variance is different Significance level 95% Bonferroni Confidence intervals for Standard Deviations Sample N StDev CI Edmonton 6 73.195 (34.1862, 260.756) Toronto 6 144.626 (78.0188, 446.084) Vancouver 6 127.296 (49.9773, 539.482) Individual confidence level = 98.3333% Tests Test Statistic Method Multiple comparisons Levene P-value 0.183 0.114 2.52 Test for Equal Variances: Edmonton, Toronto, Vancouver

Test for Equal Variances: Edmonton, Toronto, Vancouver Multiple comparison intervals for the standard deviation, a = 0.05 Edmonton Multiple Comparisons P-Value 0.183 Levene's Test P-Value 0.114 Toronto Vancouver 300 50 100 150 200 250 If intervals do not overlap, the corresponding stdevs are significantly different

d).

One-way ANOVA: Edmonton, Toronto, Vancouver Method Null hypothesis All means are equal Alternative hypothesis Not all means are equal Significance level a = 0.05 Equal variances were assumed for the analysis. Factor Information Factor Levels Values Factor 3 Edmonton, Toronto, Vancouver Analysis of Variance Source DF Adj SS Adj MS F-Value P-value Factor 2 463703 231851 16.37 0.000 Error 15 21239214159 Total 17 676094 Model Summary S R-sq R-sq(adj) 118.993 68.59% 64.40% R-sq(pred) 54.76% Means Factor Edmonton Toronto Vancouver N 6 6 6 Mean StDev 582.5 73.2 366.7 144.6 759.2 127.3 95% CI (479.0, 686.0) (263.1, 470.2) (655.6, 862.7) Pooled StDev = 118.993 Interval Plot of Edmonton, Toronto, ...

e). yes, there is significant difference between three major cities. since p-value is < 0.05.

Interval Plot of Edmonton, Toronto, ... 95% CI for the Mean Data 200 Vancouver Edmonton Toronto The pooled standard deviation is used to calculate the intervals.

f).

Tukey Pairwise Comparisons Grouping Information Using the Tukey Method and 95% Confidence Factor N Mean Grouping Vancouver 6 759.2 A Edmonton 6 582.5 A Toronto 6 366.7 B Means that do not share a letter are significantly different Tukey Simultaneous Tests for Differences of Means Difference SE of Difference of Levels of Means Difference 95% CI T-Value Toronto - Edmonton -215.8 68.7 (-394.1, -37.5) 3.14 Vancouver - Edmonton 176.7 68.7 (-1.6, 355.0) 2.57 Vancouver - Toronto 392.5 68.7 (214.2, 570.8) 5.71 Adjusted P-value 0.017 0.053 0.000 Individual confidence level = 97.97% Tukey Simultaneous 95% Cls Interval Plot of Edmonton, Toronto, ...

Tukey Simultaneous 95% Cls Difference of Means for Edmonton, Toronto, ... Toronto - Edmonton - Vancouver - Edmonton - - Vancouver - Toronto - -500 -250 250 500 If an interval does not contain zero, the corresponding means are significantly different.

iii).

Tukey Simultaneous Tests for Difference Difference of Levels of Means Toronto - Edmonton -215.8 Vancouver - Edmonton 176.7 Vancouver - Toronto 392.5 Individual confidence level - 97.97%

g).

i). Yes, there is significant difference

ii). No

iii). Yes, there is significant difference

Vancouver is largest.