This chapter introduces three methods for constructing confidence intervals using z-values, t-values, and proportions. It also describes two methods for determining sample sizes needed for confidence intervals based on probability or a given proportion. Four example problems demonstrate confidence intervals using the three construction methods, and two cover determining sample sizes, one for each sizing method. One example constructs a 98% confidence interval for a population mean based on a sample of 49 charity contributions with sample mean $150 and standard deviation $20.

1. Chapter Problems: In this chapter, confidence intervals are introduced. There were 3 different
methods of constructing a confidence interval, using a z-value, a t-value and with a proportion.
There were also 2 methods of determining how large a sample size would be required to
construct a confidence interval with the given parameters. One was done using the probability
and the other using the given proportion. Below there are 4 confidence interval problems which
will cover all three methods and 2 sample size problems, one for each method.
12. The Internal Revenue Service is studying contributions to charity. A random sample of 49
returns is selected. The mean contribution is $150 and the standard deviation of the sample is
$20. Construct a 98 percent confidence interval for the population mean.
Solution
a=0.02, |Z(0.01)|=2.58 (check standard normal table)
So 98% CI is
xbar ± Z*s/n
--> 150± 2.58*20/7
--> (142.6286, 157.3714)