Question

Physicians at a clinic gave what they thought were drugs to 920 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 51 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.46. For the hypotheses that the proportion who improve is 0.46 against that it is greater than 0.46, find the P-value.

P-value =

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of ?=1300 registered voters and found that 670 would vote for the Republican candidate. Let ? represent the proportion of registered voters in the state who would vote for the Republican candidate.
We test

?0:?=.50
??:?>.50

(a) The test statistic is ? =

(b) P-value =

Answer 1

a)

Test statistics

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

= 0.51 - 0.46 / sqrt [ 0.46 ( 1 - 0.46) / 920 ]

= 3.04

p-value = P(Z > z)

= p(Z > 3.04)

= 0.0012

b)

i)

Sample proportion = 670 / 1300 = 0.5154

Test statistics

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

= 0.5154 - 0.50 / sqrt [ 0.50 * 0.50 / 1300 ]

= 1.11

ii)

p-value = P(Z > z)

= P(Z > 1.11)

= 0.1335