Question

1) Physicians at a clinic gave what they thought were drugs to 860 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 53 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is .51 For the hypotheses that the proportion of improving is 0.51 against that it is >0.51 find the p-value.

P-value =

2)  Physicians at a clinic gave what they thought were drugs to 810 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 .45 Test the hypotheses that the proportion of patients improving is >0.45

Find the test statistics:

z =

Find the P-value

P =

Answer 1

1)

Test statistics

z = ( - p) / sqrt [ p (1 - p) / n ]

= ( 0.53 - 0.51 ) / sqrt [ 0.51 ( 1 - 0.51) / 860 ]

= 1.17

For right tailed test,

p-value = P(Z > z)

= P(Z > 1.17)

= 0.1210

b)

Test statistics

z = ( - p) / sqrt [ p (1 - p) / n ]

= (0.50 - 0.45 ) / sqrt [ 0.45 ( 1 - 0.55) / 810 ]

= 2.86

For right tailed test,

p-value = P(Z > z)

= P(Z > 2.86)

= 0.0021