(1 point) Family transportation costs are usually higher than most people believ

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 0.05 Edmonton Toronto Vancouver 480 550 G00 675 700 950 780 175 (a) Specity the appropriate statistical hypotheses. A. HO: The three popuation means are the same. HA: All three means are different from the others. B. HO: The three population means are the same. HA At least one of the means is difTerent from the others C. HO: At least one of the means is different from the others. HA: The means are the same. In order to obtain valid inferences trom the one-way ANOVA procedure, check the assumptions need to be reasonably satistied. b) Do the data collected from each city tollow approximately Normal distribution? (C) Can the population variances be reasonably assurned to be the sarne? ? () Report your Levene's test of equal variance test statistic value. Use two decimal places. (i) Report the - value of your Levene's test of equal variance. Use three decimal places. d) Complete the tol owing one-way ANOVA table. Source Degrees of Freedom Sum of Squares Mean Square p- valute City Error Total (e) Do the data suggest that there is a significant overall difference of transportation costs between these three ajor cities? ? Suppose that there is a significant overall difference. Use the Tukey's tests to find which pair of average transportation costs are significantly different. Use =0.05 . 0) What is the critical value from the studentized range distribution you used to calculate the Tukey's test statistic value? Use two decimal places (i) What is your Tukey's test statistic value. Use three decimal places. i Use 1 decimal place, the absolute differences for all three poss ble pairwise liToronro Vancoule (g) ls there a significant difference of transportation costs between Edmonton and Toronto? Edmonton and Vancouver? 7 Toronto and Vancouver?

Explanation / Answer

Step 1

null, Ho: µ1 =µ2 =µ3

alternative, H1: three means are diffrent from the others

Step 2

Degrees of freedom between = k - 1 = 3 - 1 = 2

Degrees of freedom Within = n - k = 18 - 3 = 15

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.682

Step 3

Grand Mean = G / N = 582.5+366.667+759.167 / 3 = 569.445

SST = ( Xi - GrandMean)^2 = (650-569.445)^2 + (480-569.445)^2 + (550-569.445)^2 + ……..& so on = 676094.444

SS Within = (Xi - Mean of Xi ) ^2 =,(650-582.5)^2 + (480-582.5)^2 + (550-582.5)^2 + ……..& so on = 212391.667

SS Between = SST - SS Within = 676094.444 - 212391.667 = 463702.777

Step 4

Mean Square Between = SS Between / df Between = 463702.777/2 = 231851.389

Mean Square Within = SS Within / df Within = 212391.667/15 = 14159.444

Step 5

F Cal = MS Between / Ms Within = 231851.389/14159.444 = 16.374

We got |F cal| = 16.374 & |F Crit| =3.682

MAKE DECISION

Hence Value of |F cal| > |F Crit|and Here We Reject Ho

Treatments ONE WAY ANOVA Mean = X /n 1 650 480 550 600 675 540 582.5 2 250 525 300 175 500 450 366.667 3 850 700 950 780 600 675 759.167

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