how to calculate 99.99% confidence interval in matlab

To calculate the 99.99% confidence interval in Matlab, we can use the norminv function which returns the value of the inverse cumulative distribution function (CDF) of a standard normal distribution. The formula to calculate the confidence interval is:

main.m
confidence_interval = [mean - z * (sigma / sqrt(n)), mean + z * (sigma / sqrt(n))];
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where mean is the sample mean, sigma is the sample standard deviation, n is the sample size, and z is the critical value of the standard normal distribution for the given confidence level.

For a 99.99% confidence level, z can be calculated as:

main.m
z = norminv((1 + 0.9999)/2, 0, 1);
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Here, 1 + 0.9999 is divided by 2 because we are interested in the two-tailed test. The second and third arguments of the norminv function correspond to the mean and standard deviation of the standard normal distribution, which are 0 and 1 respectively.

Putting it all together, we can write the following Matlab code to calculate the 99.99% confidence interval:

main.m
% Sample data
data = [1.2, 2.5, 3.1, 2.8, 4.0, 1.7, 2.2, 3.5, 1.9, 2.4];

% Sample mean and standard deviation
mean_data = mean(data);
std_data = std(data);

% Sample size
n = length(data);

% Critical value for 99.99% confidence level
z = norminv((1 + 0.9999)/2, 0, 1);

% Confidence interval
confidence_interval = [mean_data - z * (std_data / sqrt(n)), mean_data + z * (std_data / sqrt(n))];
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The confidence_interval variable now contains the lower and upper limits of the 99.99% confidence interval.