Question

(1 pt) Physicians at a clinic gave what they thought were drugs to 850 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 50 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.45. For the hypotheses that the proportion who improve is 0.45 against that it is greater than 0.45, find the P-value.

P-value =

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.45

H_a : p > 0.45

= 0.50

n = 850

P₀ = 0.45

1 - P₀ = 0.55

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.50 - 0.45 / [(0.45 * 0.55) / 850]

= 2.93

= (z > 2.93) = 1 - P(z < 2.93) = 0.0017

P-value = 0.0017