Question

Here is the question: Dr Oz told us that control group had 31 patients. Likely the test group also had 31 patients. Thus 17 out of 31 (55%) in control group improved, and 25 out of 31 (81%) in test group improved. (1) Given the data, what is the p-value for the hypothesis test where the null hypothesis is “hydroxychloroquine makes no difference”? (2) If you want to argue that Dr. Oz made the correct conclusion that these results were “statistically significant”, what is your argument? (3) If you want to argue that Dr. Oz made the wrong conclusion, what is your argument?

Answer 1

(1)

Null hypothesis H0: True proportion of patients improved with and wihout hydroxychloroquine are equal.

Alternative hypothesis Ha: True proportion of patients improved with and wihout hydroxychloroquine are not equal.

Pooled proportion, p = (17 + 25) / (31 + 31) = 0.6774194

Standard error of mean difference SE =

= 0.1187359

Test statistic z = (p2 - p1) / SE = (0.81 - 0.55)/0.1187359 = 2.19

For two tail test, p-value = 2 *P(z > 2.19) = 0.0285

(2)

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that true proportion of patients improved with and wihout hydroxychloroquine are not equal.

Dr. Oz has made the correct conclusion that these results were “statistically significant”,

(3)

For one tail test, p-value = P(z > 2.19) = 0.0143 which is less than 0.05 significace level and shows that the true proportion of patients improved with hydroxychloroquine are greater than the proportion of patients improved withour. hydroxychloroquine

We can argue that hydroxychloroquine significantly increases the proportion of improved cases.