Confidence Intervals Worksheet

Part I.

A local animal shelter wants to know the proportion of dogs that get adopted out of all the animals in the shelter.A random sample of 150 customers is taken and 85 adopted a dog.

1.Construct a 93% confidence interval for the proportion of dog adoptions.

2.What is the margin of error at 93% confidence?

3.Construct a 93% confidence interval for the proportion of dog adoptions for a random sample of 235 customers.How does the size of this interval change from the interval in #1 above?

4.How large of a sample is required to be taken for the error of the estimate (margin of error) to be within + .04 of the population proportion.

Part II.

In a study designed to test the effectiveness of acupuncture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The numbers of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2.

1. A.Construct a 99% confidence interval estimate of the mean number of migraine attacks for

those treated with acupuncture.

B.Interpret this interval in the context of this problem.

C.How many subjects treated with acupuncture need to be sampled to keep the error of the

estimate within + .5 of the population mean?Use = 1.3.

1. A. Construct a 99% confidence interval estimate of the mean number of migraine attacks for

those given a sham treatment.

B.Interpret this interval in the context of this problem.

C.How many subjects given the sham treatment need to be sampled to keep the error of the

estimate within + .5 of the population mean?Use = 1.1.

1. Compare the two confidence intervals. Do the results suggest the effectiveness of one method over the other?