Question

Part 1 One-way ANOVA (35 points) A rental car company wants to investigate whether the type of car rented affects the length of the rental period. An experiment is run for one week at a particular location, and 4 rental contracts are selected at random for each car type. The results are shown in the following table. Car type Observations (# of days) Compact Midsize 7 3 16 15 6 8 7 9 Full size A. Is there evidence to support a claim that the type of car rented affects the length of the rental contract? Assumption of normality is fulfilled. Use a = 0.05. (15 points)

Only Answer Part B please.

Answer 1

Solution:

(A) Null and alternative hypothesis Ho: U1= U2=u3 H: Not all the means are equal. ANOVA length of rental period Sum of Squares df Between Groups 37.500 Within Groups 38.500 Total 76.000 11 Mean Square 18.750 4.278 F 4.383 Sig. .047 The p-value of F- test statistic is less than 0.05. Hence we reject Ho at 0.05 level of significance and conclude that there is evidence to support a claim that the type of car rented affects the length of the rental contract.

(B) Multiple Comparisons | Dependent Variable: length of rental period (I) car type (1) car type Mean Difference (I-1) Std. Error Compact Bonferroni Midsize Midsize Full size Compact Full size Compact .091 .54 Full size .000 -3.750 .000 -3.750 3.750 3.750 .000 -3.750 .000 -3.750 3.750 3.750 Midsize Sig | 95% Confidence Interval Lower Upper Bound | Bound 1.000 4.29 4.29 091 -8.04 54 1.000 4.29 4.29 -8.04 .091 - 54 8.04 091 - 54 8.04 1.000 4.27 4.27 -8.02 1.000 4.27 4.27 089 -8.02 52 089 8.02 089 -52 1.462 1.462 1.462 1.462 1.462 1.462 1.462 1.462 1.462 1.462 1.462 1.462 Compact Sidak .089 52 Midsize Midsize | Full size Compact Full size Compact Midsize Full size 8.02 We find the significance difference in ANOVA table (part A) but the result of Bonferroni and Sidak test doesn't shows the significant difference in length of rental period between two car types namely, Compact & Midsize, Compact & Full size and Midsize & Full size. All the three type of pairs has p-value greater than 0.05. But on the basis of mean difference in length of rental period we can say that Full size car type is responsible for difference.