1. Using the annual precipitation data at Tucson

a. Compute the 95% and 99% confidence interval for the sample mean for the cases where the variance is known and for the case when it is unknown.

b. Compute the 95% and 99% confidence intervals for the sample variance.

c. Determine the sample size if you want the precision for the Tucson annual precipitation sample mean to be 10%.

d. Compute the Type II error if the true mean is 10% larger than the sample mean

2. Use the annual maximum flows at the Rio Grande at Embudo to:

a. Test the hypothesis that the peaks after 1965 have a different mean than those before that year. Use a confidence level of 5%.

b. Test if the variance has changed in the period 1966-present.

**Subject Engineering MATLAB for Engineering**