Question

To test the effectiveness of a new drug, a researcher gives one group of individuals the new drug and another group a placebo. The results of the study are shown in the following table. At α=0.05, can the researcher conclude that the drug is effective? (Use Chi-Square testing procedure) Effective Not Effective Drug 32 9 Placebo 12 18 (a) State the null and alternative hypothesis for this test. (b) Calculate the test statistic and the critical value. (c) Report the p-value, and state your conclusion in words.

Answer 1

a) H0: The drugs is not effective.

H1: The drugs are effective.

b)

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	Effective	Not effective	Total
Drug	32	9	41
Placebo	12	18	30
Total	44	27	71

O	E	(O-E)	(O-E)^2	(O-E)^2/E
32	25.40845	6.591549	43.44852	1.710003
9	15.59155	-6.59155	43.44852	2.786671
12	18.59155	-6.59155	43.44852	2.337004
18	11.40845	6.591549	43.44852	3.808451
			Total	10.64

c)

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (2 - 1) = 1 * 1 = 1

P-value = P( ) = 0.0011

P-value < 0.05 we reject null hypothesis.

Conclusion:

The drugs are effective.