Final answer:
To estimate the distribution of a dataset in MATLAB, use histogram, fitdist, or mle. A goodness-of-fit test such as chi2gof validates the distribution choice. Then, construct confidence intervals using norminv, with the confidence level, sample mean, and standard error.
Step-by-step explanation:
To estimate the distribution and its parameters of a set of observations X in MATLAB, one might start by plotting a histogram using the histogram function. This visual representation can provide insights into the shape of the data distribution. To define the distribution, one could use various MATLAB functions, such as fitdist for fitting a probability distribution object to the data, or mle for maximum likelihood estimation of distribution parameters.
After selecting an appropriate distribution, a goodness-of-fit test like the Chi-square or Kolmogorov-Smirnov test can help determine the suitability of the chosen distribution. In MATLAB, functions like chi2gof can be used for the Chi-square test. These tests establish a null hypothesis that the data is drawn from the specified distribution. Rejecting or failing to reject this hypothesis with a provided p-value supports the conclusion about distribution fit.
Next, to construct a confidence interval for a population mean, assuming the chosen distribution is normal, one can use the norminv function to find the z-scores for the desired confidence level, then compute the interval using the sample mean and the standard error of the mean. The confidence interval is stated, a corresponding graph can be plotted, and the error bound is calculated.