Question

Five different brands of tyres used by a car rental agency in the process of deciding the brand of tyre to purchase as standard equipment for their fleet, found that each of five tyres of each brand last the following number of kilometers (in ‘000): Tyre Brand A B C D E 36 46 35 45 41 37 39 42 36 39 42 35 37 39 37 48 37 43 35 35 47 48 38 32 38 Perform a one – way analysis of variance to test the hypothesis that the five different brands of tyres have identical average life.

Answer 1

To test the hypothesis that the five different brands of tires have identical average life, we can perform a one-way analysis of variance (ANOVA). ANOVA compares the means of multiple groups to determine if there is a significant difference between them.

Step-by-step explanation:

To test the hypothesis that the five different brands of tires have identical average life, we can perform a one-way analysis of variance (ANOVA). ANOVA compares the means of multiple groups to determine if there is a significant difference between them. In this case, the five different brands of tires are treated as the groups.

Here are the steps to perform a one-way ANOVA:

1. State the null and alternative hypotheses.
2. Calculate the sum of squares between groups (SSB), sum of squares within groups (SSW), and total sum of squares (SST).
3. Calculate the degrees of freedom for SSB and SSW.
4. Calculate the mean square between groups (MSB) and mean square within groups (MSW).
5. Calculate the F-statistic by dividing MSB by MSW.
6. Determine the critical value for the F-statistic at the chosen significance level.
7. Compare the F-statistic to the critical value to make a decision.

Using the given data, we can perform the calculations to complete the one-way ANOVA and determine if the five different brands of tires have identical average life.