Question

Physicians at a clinic gave what they thought were drugs to 820 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 58 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.56. For the hypotheses that the proportion of improving is 0.56 against that it is >0.56, find the p-value.

Answer 1

Hypothesis :

Right tailed test.

Test statistic :

n = 820 , = 0.58 , P = 0.56

P-value :

P-value for this right tailed test is ,

P-value = P( z > z_stat ) = P( z > 1.1538 )

P( z > 1.1538 ) = 1 - P( z < 1.1538 )

Using Excel function , =NORMSDIST( Z )

P( z < 1.1538 ) = NORMSDIST(1.1538 ) = 0.875709

So, P-value = 1 - 0.875709 = 0.1243

P-value = 0.1243