Instructions: Perform what is being asked. (30 points) 1. The side effects of a new drug are being tested against a placebo. A simple random sample of 565 patients yields the results below. At a significance level of a = 0.10, is there enough evidence to conclude that the treatment is independent of the side effect of nausea? Result Drug Placebo Total Nausea 36 13 49 No nausea 254 262 516 Total 290 275 1565 a. The null hypothesis Ho: the treatment and response are independent. b. The alternative hypothesis Ha: the treatment and response are dependent. c. The level of significance a = 0.01 d. The degrees of freedom: (2 - 1) x (2 - 1) = 1 x 1 = 1 e. The test statistic can be calculated using a table: Row, Column E O E - 0 (0 - E) (0 - E) E 1,1 -108 - 29.19 36 10.85 117.72 4.681 1,2 49 x275 =23.85 13 -10.85 117.72 4.936 565 2,1 516 x290 = 264.85 254 -10.85 117.72 0.444 565 2,2 516 X275 =251.15 262 10.85 117.72 0.469 565 x 2 (0 - E)2 E a. The critical value: From = 0.01 and k - 1 = 1, the critical value is 2.706 b. Decision: Since ** ~ 10.53 > 2.706, there is enough statistical evidence to reject the null hypothesis and to believe that there is a relationship between the treatment and response