Question

Physicians at a clinic gave what they thought were drugs to 990 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 0.48. Test the hypotheses that the proportion of patients improving is >0.48.

Find the p-value.

p=

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.48

H_a : p > 0.48

n = 990

=0.50

P₀ = 0.48

1 - P₀ = 1 - 0.48 = 0.52

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.50 - 0.48/ [0.48- 0.52 / 990 ]

=  1.26

Test statistic = z =1.26

P(z > 1.26 ) = 1 - P(z < 1.26) = 1 - 0.8962

P-value = 0.1038