**1. **A random sample of 93 observations produced a mean x=25.5 and a standard deviation sequals=2.4.

**a. **Find a 95% confidence interval for μ.

**b. **Find a 90% confidence interval for μ.

**c. **Find a 99% confidence interval for μ.

**2.** The mean and standard deviation of a random sample of n measurements are equal to 34.4 and 3.6, respectively.

**a.** Find a 90% confidence interval for μ if n=121.

**b.** Find a 90% confidence interval for μ if n=484.

**c. **Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

**3.** If you wish to estimate a population mean with a margin of error ME=0.23 using a 95% confidence interval and you know from prior sampling that σ2 is approximately equal to 7.3, how many observations would have to be included in your sample?

The number of observations that would have to be included in your sample is