 # Statistical Hydrology

## Question

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.

## Solution Preview

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matrix = xlsread('TucsonAnnualPrecip2014.xlsx');

data = matrix(:,2);
mu = mean(data);
sigma = std(data);
variance = sigma^2;
n = length(data);
sigma_n = sigma/sqrt(n);

%Variance is known -- normal distribution
Z_normal_95 = 1.96;
Z_normal_99 = 2.58;

%Variance is unknown -- t distribution
%Values obtained from t table
Z_t_95 = 2.011;
Z_t_99 = 2.682;

%%%
%%% Problem 1 a)
%%%...
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