How long do new batteries last on a camping trip? A random sample of n1 = 42 small camp flashlights were installed with brand I batteries and left on until the batteries failed. The sample mean lifetime was x1 = 9.8 hours with sample standard deviation s1 = 2.2 hours. Another random sample of n2 = 38 small flashlights of the same model were installed with brand II batteries and left on until the batteries failed. The sample mean of lifetimes was x2 = 8.1 hours with sample standard deviation s2 = 3.5 hours.
1. Should you use the critical value (zc) or (tc) in determining a confidence interval in this problem? Explain.
2. Find a 90% confidence interval for the population difference m1 - m2 of lifetimes for these batteries.
3. Does the confidence interval in part (b) contain all positive, all negative, or both positive and negative numbers? What does this tell you about the mean life of battery I compared to battery II?