Can you provide detail explanation of each step and solutions please.

The National Institutes of Health announced on October 31, 1995, the results of a study of the effectiveness of thalidomide in healing mouth ulcers in AIDS patients. In the study, which was chaired by Dr. Jeffrey Jacobson of the Bronx Veteran Affairs Medical Center and the Mount Sinai School of Medicine in New York, it was found that 14 of 23 patients who received thalidomide had their ulcers heal, compared with 1 of 22 patients who received a placebo.

(a) Determine if there is a difference between the proportion of people who have their ulcers heal while taking thalidomide versus a placebo by doing a hypothesis test at the 5% level via the following the following steps.

	i. Write down appropriate null and alternative hypotheses, defining any parameters that you mention.
	ii. State the formula of the test statistic to be used.
	iii. State the reference distribution (the distribution of the test statistic) if the null hypothesis is true.
	iv. Calculate the value of the test statistic and find the P-value.
	v. Should H0 be retained or rejected? Why?

(b) Obtain a 95% confidence interval for p₁p₂.

(c) Explain the meaning of your conclusions in detail.