Question

A tech company wants to estimate the average battery life for one of their new line of laptops. In previous models, the average battery life was 5.75 hours. They believe that, due to some improvements, the average battery life for this new line is 7 hours. They collect a random sample of 100 laptops and find the average battery life is 6.23 hours with a standard deviation of 1.97 hours. Find a 99% confidence interval for the true average battery life of this laptop. Using your results, is there evidence that the average battery life has improved? If so, has it improved to be as much as 7 hours? Relate your confidence interval to the set-up of the problem and explain your reasoning.

Answer 1

df = n - 1 = 100 - 1 = 99

t criitcal value at 0.01 significance level with 99 df = 2.626

99% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

6.23 - 2.626 * 1.97 / sqrt(100) < < 6.23 + 2.626 * 1.97 / sqrt(100)

5.71 < < 6.75

99% CI is ( 5.71 , 6.75 )

Since 5.75 contained in confidence interval, we do not have sufficient evidence to conclude that

the average battery life has improved

Since all values in confidence interval are less than 7 , we do not have sufficent evidence to support

the claim.