Question

1. Family transportation costs are usually higher than most people believe because those costs include car payments, insurance, fuel costs, repairs, parking, and public transportation. Twenty randomly selected families in four major cities are asked to use their records to estimate a monthly figure for transportation cost.
   1. Use the data obtained and ANOVA to test whether there is a significant difference in monthly transportation costs for families living in these cities. Assume that α = .05. Report a p-value and interpret the results of the statistical test.
   2. Use α= 0.05, and construct confidence intervals for all pairs of differences between means. Which of these differences, if any, are statistically significant at the selected significance level?

Atlanta	New York	Los Angeles	Chicago
650	250	850	540
480	525	700	450
550	300	950	675
600	175	780	550
675	500	600	600

Answer 1

minitab<stat<anova<one way anova

Results for: Worksheet 2

One-way ANOVA: Atlanta, New York, Los Angeles, Chicago

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 4 Atlanta, New York, Los Angeles, Chicago

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 3 456630 152210 11.03 0.000
Error 16 220770 13798
Total 19 677400

Model Summary

S R-sq R-sq(adj) R-sq(pred)
117.465 67.41% 61.30% 49.08%

Means

Factor N Mean StDev 95% CI
Atlanta 5 591.0 78.5 (479.6, 702.4)
New York 5 350.0 155.1 (238.6, 461.4)
Los Angeles 5 776.0 134.6 (664.6, 887.4)
Chicago 5 563.0 82.7 (451.6, 674.4)

Pooled StDev = 117.465

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
Los Angeles 5 776.0 A
Atlanta 5 591.0 A B
Chicago 5 563.0 B
New York 5 350.0 C

Means that do not share a letter are significantly different.

a) since p-value =0.000

since p-value is less than level of significance so we reject null hypothesis.

so there is significant difference between means.

b) there significant difference between pair of means

los Angeles and chigago and los Angeles and newyork

Altanta and newyork

chicago and newyork