math homework help

6 points

1. 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?

2. Two pain relief drugs are being considered. A random sample of 8 doses of the first drug showed that the average amount of time required before the drug was absorbed into the bloodstream was x1 = 24 minutes with population standard deviation = 4 minutes. For the second drug, a random sample of 10 doses showed the average time required for absorption was x2 = 29 minutes with population standard deviation = 3.9 minutes. Assume the absorption times follow a normal distribution.

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 difference in average absorption time for the two drugs.

3. Does it appear that one drug is absorbed faster than the other (at the 90% level)? Explain.