A laptop computer manufacturer found that by improving their battery design, they could increase the time that the laptop computer could be used on a single charge. To verify this improvement, they compared a sample of 10 laptops installed with the improved batteries to a control group of 10 laptops installed with current batteries. After subjecting each laptop to a predetermined set of operations until it ceased to operate, they found that the average lifespan of the improved battery was 4.31 hours, and that the average lifespan of the current battery was 3.68 hours. Correspondingly, the sample standard deviation for the improved batteries was 0.17 hours for the improved group and the sample standard deviation for the current group was 0.22 hours.

Question

Assuming that the two groups have unequal variances, calculate the t-statistic that tests the null hypothesis that the mean lifespan of the two types are equal against the alternative hypothesis that the mean lifespan for the improved batteries is greater than that for the current batteries.
a)1.62
b)7.166
c)-3.682
d)6.907
e)4.923

Answer 1

Welch's t-test for unequal variances:

t = (mean1 - mean2)/√(s^2/n1 + s^2/n2)

t = (4.31 - 3.68)/√(0.17^2/10 + 0.22^2/10)

t = 0.63/0.08792 = 7.166 (rounded)