Answer the following using MATLAB code:

In designing an experiment, compute power of a hypothesis test and determine the sample size needed to ensure statistical significance and power

Your code may use the following MATLAB commands $```$ mean, std$,$ cdf$,$ icdf$```$ and normal functions for computing $(`$length$`,`$inv$`,`$sqrt$`,...),$ but otherwise $*$no built$-$in functions for statistics$*.$

$*$Read the questions carefully and name variables of solutions as specified.$*$

Researchers are investigating the effectiveness of a new drug designed to lower blood pressure. Five individuals with hypertension participated in a pilot study. The researchers measured the systolic blood pressure of each individual before and after they took the drug for a period of one month. The systolic blood pressure readings $($in mmHg$)$ for each individual before and after the intervention are recorded below:

Individual Before Drug $($mmHg$)$ After Drug $($mmHg$)$

$1155150$

$2160155$

$3145138$

$4150151$

$5170160$

These data and code to test the null hypothesis that this drug did not reduce systolic blood pressure can be found in the MATLAB code for this problem. Run this code and you should find that you can reject this null hypothesis $($p $=0\mathrm{.}0022),$

Q$4$a$)$ Write and execute MATLAB code to compute the power of this test to detect a drop of $5$ mmHg in pressure. $($The correct answer should be between $20\%$ and $40\%)$

Q$4$b$)$ Write and execute MATLAB code to compute the total number of subjects you expect to need to raise this power to $95\%.$ Save this value in the variable named $`$n$\_$needed$`.($The correct answer should be between $10$ and $30.)$