A phone manufacturer wants to compete in the touch screen ph

A phone manufacturer wants to compete in the touch screen phone market. Management understands that the leading product has a less than desirable battery life. They aim to compete with a new touch phone that is guaranteed to have a battery life more than two hours longer than the leading product. A recent sample of 116 units of the leading product provides a mean battery life of 5 hours and 29 minutes with a standard deviation of 40 minutes. A similar analysis of 94 units of the new product results in a mean battery life of 7 hours and 50 minutes and a standard deviation of 25 minutes. It is not reasonable to assume that the population variances of the two products are equal.

Sample 1 is from the population of new phones and Sample 2 is from the population of old phones. All times are converted into minutes. Let new products and leading products represent population 1 and population 2, respectively.

Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product.

Implement the test at the 5% significance level using the critical value approach.

Solution

1) H0: 1 2 120; HA: 1 2 > 120.........

test statistic = [ (470-329)-(120) ] / [ (25^2/94 ) + (40^2/116) ] = 21 / 4.5213 = 4.644682......

t-value = 0.000003117534........
which is less than 0.05...

So, Reject H0; the battery life of the new product is more than two hours longer than the leading product...