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 120 units of the leading product provides a mean battery life of 5 hours and 40 minutes with a standard deviation of 30 minutes. A similar analysis of 100 units of the new product results in a mean battery life of 8 hours and 5 minutes and a standard deviation of 55 minutes. It is not reasonable to assume that the population variances of the two products are equal. Let new products and leading products represent population 1 and population 2, respectively. 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.
a. Set up the hypotheses to test if the new product has a battery life more than two hours longer than the leading product.
i. H0: 1 2 = 120; HA: 1 2 =120
ii. H0: 1 2 = 120; HA: 1 2 > 120
iii. H0:1 2 =120; HA: 1 2 < 120
b-1. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
b-2. Implement the test at the 5% significance level using the critical value approach.
i. Do not reject H0; the battery life of the new product is not more than two hours longer than the leading product.
ii. Do not reject H0; the battery life of the new product is more than two hours longer than the leading product.
iii. Reject H0; the battery life of the new product is not more than two hours longer than the leading product.
iv. Reject H0; the battery life of the new product is more than two hours longer than the leading product.