Question

Solution of the Example Calculate Mean: Standard Deviation: S-- Σ(xi-x) Find the t-score: If it is 95% confidence limit (α-0.05), you can use the above Table For any other α values, use the online t-score calculator (http://stattrek.com/online-calculator/t-distribution.aspx) Input Degrees of Freedom v-N-1 and Cumulative Probability-1- (a/2), you obtain t-scores: t 1-a/2,v x-(q-a/2,V) Lower (1- a) Confidence Limit: VN Upper(1-α) Confidence Limit: x4(11-a/2,V)

Please comment code with steps

Answer 1

Define the following function and save it in confid.m (We are taking the confidence level as input and hence are not just restricting to calculating for 95%) . (If your version of matlab allows including the functions in scripts, then no need to create a function file)

Call the above function in the following code

get the following output

All code in text format

---- The function ---

%function to find the confidence interval
%The function takes the following inputs
%inputs
% x - Vector of Measurements
% CL - confidence level of the required confidence interval (in %)
%outputs
% mv - mean value
% uc - upper confidence limit
% lc - Lower confidence limit
function [mv,uc,lc]= confid(x,CL)
%find the number of observations N in the vectro x
N=length(x);
% find the sample mean
xbar=1/N*sum(x);
% find the sample standard deviation
S=sqrt(1/(N-1)*sum((x-xbar).^2));
%find the alpha for confidence level conf.level
a=1-CL/100;
%calculate the degrees of freedom
df=N-1;
%find the critical value of t
tcrit=tinv(1-a/2,df);
%calculate the lower (1-alpha) confidence limit
lc=xbar-tcrit*S/sqrt(N);
%calculate the upper (1-alpha) confidence limit
uc=xbar+tcrit*S/sqrt(N);
% assign xbar to mv, to output the mean value
mv=xbar;
end

%---The main ----

%set the measurement vector
x=[19.1 22.2 16.9 19.4 20.2 18.0 21.1];
% assign the confidence level
cl=95;
% call the function to get the confidence interval
[mv,uc,lc]= confid(x,cl);
%print the results
fprintf(' The mean value is %.2f, and %d%% confidence interval for mean is [%.3f,%.3f] ',mv,cl,lc,uc);