function [low,high] = pred_int(x,alpha)

%PRED_INT_MEAN computes the sample mean and standard deviation for data x, and 
%uses this to compute the 100*(1-alph) percent prediction interval for a new 
%sample (default = 95%), denoted by the values [low,high].

%INPUTS:      x = data vector
%         alpha = (optional) value of alpha (default = .05)

if nargin == 1
    
    alpha = .05;
    
end

x_bar = mean(x);

sig = std(x);

n = length(x);

% *************

% x_bar = 7.321; Data from Assignment 4
% 
% sig = .1498;
% 
% n = 7;

%*************

t = abs(tinv(alpha/2,n-1));

low = x_bar - t*sig*sqrt(1 + (1/n));

high = x_bar + t*sig*sqrt(1 + (1/n));