# confidence interval questions! i'm confuse

• Mar 4th 2007, 07:25 AM
Nizzle_dazzel
confidence interval questions! i'm confuse
4. Among 5000 items of randomly selected baggage handled by the American airline 22 were lost. Among 4000 items handled by delta airlines, 15 were lost. Use the sample data to construct a 95% confidence interval estimate of the difference between the two rates of lost luggage. Based on the result, does there appear to be a difference between the two rates of lost baggage. Why or why not?
5. A randomized trial tested the effectiveness of diets on adults. Among 40 subjects using the weight watcher diet, the mean weight loss after one year was 3.0lbs with a standard deviation of 4.9lb among the 40 subjects using Atkins diet the mean weight loss after one year was 2.1 lb with standard deviation of 4.8 lb. construct a 95% confidence interval estimate of the difference in the effectiveness of the two diets. Does the amount of weight loss appear to justify the diet?
• Mar 5th 2007, 07:51 PM
CaptainBlack
Quote:

Originally Posted by Nizzle_dazzel
4. Among 5000 items of randomly selected baggage handled by the American airline 22 were lost. Among 4000 items handled by delta airlines, 15 were lost. Use the sample data to construct a 95% confidence interval estimate of the difference between the two rates of lost luggage. Based on the result, does there appear to be a difference between the two rates of lost baggage. Why or why not?

The estimated rate of loss of bags by American is:

pa=22/5000,

with sd:

sa=sqrt(pa(1-pa)/5000)

(as the number n lost is actualy ~b(n;5000,PA), where PA is the actual probability that A loses a bag which we estimate by pa).

The equivalent for Delta are:

pd=15/4000,

and

sd=sqrt(pd(1-pd)/4000).

Now you are expected to treat x=pa-pd as a normal random variable with standard deviation s=sqrt(sa^2+sd^2), and construct the 95% confidence interval for this. This is [(pa-pd)-1.96s,(pa-pd)+1.96s], if this interval does not include 0 we would construe this as supporting the idea that there is a difference in the bagage loss rates of the two airlines, otherwise that the difference is not statisticaly significant.

RonL