Question

The following sample data represents the life cycle in months of two car batteries:

A: 62, 59, 59, 51, 55, 53, 58, 49, 61, 55

B: 45, 50, 47, 46, 48, 46, 45, 46, 51, 49, 47, 49, 48, 45, 57

Is the variation in life cycle the same between batteries at lambda=.05? Are the means the same as well at lambda=.05? Which battery would you choose and why?

Answer 1

First we will calculate the sample mean and sample variance for the 2 data sets:

For Battery A:

For Battery B:

Test for variance equality:

Variation in life cycle is same between batteries A and B

Test for equality of mean:

Since the two means are different and we know that the mean of battery A is greater than mean of Battery B therefore we will again test our hypothesis by changing the alternate hypothesis to mean of battery A is greater than mean of Battery B.
We get the following result:

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ1​ = μ2​

Ha: μ1​ > μ2​

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Therefore I will prefer Battery A because it has a greater mean life.

Please up vote if you like the solution.Thanks.