Explore the t-distribution by the following procedure: a. Draw a sample of n poi

Question

Explore the t-distribution by the following procedure: a. Draw a sample of n points from the standard normal distribution. b. Compute the mean and standard deviation of this sample. c. Form the statistic t = (x bar - mu)/(s/squareroot n) where x bar and s are the mean and the standard deviation computed in (b), mu = 0 (standard normal distribution) and n = 20. Store this value d. Repeat steps (a)-(c) about 5000 times. e. Plot the histograms of the statistic and verify visually that it looks like a t-distribution. Determine the two-sided probabilities associated with 60%, 70%, 80%, 90%, 95% and 99%. (We have been working exclusively with two-sided probabilities in this class). f. Repeat the process a-e for various values of n (degrees of freedom) (Some relevant MATLAB functions: randn, mean, std, hist, prctile)

Explanation / Answer

(a)

%Initialize n to any number.

r=randn(n)

(b)

%To find mean and standard deviation

mean_r=mean(r);

std_r=std(r);

(c)

%To compute statistic t

r=randn(20)

mean_r=mean(r)

std_r=std(r)

t=mean_r/(std_r*sqrt(20))

(d)

for i=1:5000

r=randn(20)

mean_r=mean(r)

std_r=std(r)

t=mean_r/(std_r*sqrt(20))

end

(e)

n=20;

t=[]

for i=1:5000

r=randn(n);

mean_r=mean(r);

std_r=std(r);

t(i)=mean_r/(std_r*sqrt(20));

end

%Plot histogram

hist(t)

(f)

You can change thae values of n.

function []=plothistrandomvalues(n)

  r=randn(n)

for i=1:5000

mean_r=mean(r)

std_r=std(r)

t=mean_r/(std_r*sqrt(20))

end

hist(t)

end

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