Question

All new drugs must go through a drug study before being approved by the U.S. Food and Drug Administration (FDA). A drug study typically includes clinical trials whereby participants are randomized to receive different dosages as well as a placebo but are unaware of which group they are in. To control as many factors as possible, it is best to assign participants randomly yet homogeneously across the treatments. Consider the following arrangement for homogeneity with respect to gender and dosages.

Gender	10-mg Drug	20-mg Drug	Placebo
Female	56	53	61
Male	30	30	25

(a) At the 0.01 level of significance, is the distribution of drug the same for both genders?
(i) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)

(iii) State the appropriate conclusion.

Fail to reject H₀. There is sufficient evidence to show that the distribution is not proportioned the same for each drug at the 0.01 level of significance. Reject H₀. There is sufficient evidence to show that the distribution is not proportioned the same for each drug at the 0.01 level of significance.     Reject H₀. There is not sufficient evidence to show that the distribution is not proportioned the same for each drug at the 0.01 level of significance. Fail to reject H₀. There is not sufficient evidence to show that the distribution is not proportioned the same for each drug at the 0.01 level of significance.

(b) Considering the same study, homogeneity of ages would also be an important feature. At the 0.01 level of significance, is the distribution of drug that follows the same for all age groups?

Age	10-mg Drug	20-mg Drug	Placebo
40−49	18	22	17
50−59	51	39	56
60−69	17	22	13

(i) Find the test statistic. (Give your answer correct to two decimal places.)(ii) Find the p-value. (Give your answer bounds exactly.)
  
(iii) State the appropriate conclusion.

Answer 1

Question 1) Solution:

(i) the test statistic=1.09

(ii) the p-value = 0.5794

0.5<p value < 0.9

iii) Fail to reject H0. There is not sufficient evidence to show that the distribution is not proportioned the same for each drug at the 0.01 level of significance.

Question 2) Solution:

i) the test statistic 6.21

ii) P value is 0.1842

0.1 < p value < 0.5

iii) We fail to reject H0.

We do not have sufficient evidence to say that,the distribution of drug that follows the same for all age groups