Physicians at a clinic gave what they thought were drugs to 860 patients. Although the doctors later learned that the drugs were really placebos, 59% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.55. Test the hypotheses that the proportion of patients improving is >0.55

Find the test statistics:

z=

Find the p-value.

p=

Question

Mathematics

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8 September, 00:59

Physicians at a clinic gave what they thought were drugs to 860 patients. Although the doctors later learned that the drugs were really placebos, 59% of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.55. Test the hypotheses that the proportion of patients improving is >0.55

Find the test statistics:

z=

Find the p-value.

p=

+2

Answers (1)

Know the Answer?

Pennington · Answer 1

Z=2.36

P=0.0091

Step-by-step explanation:

The hypothesis is:

π > 0.55 which is the population proportion

The formula to get the test statistic is

Zstat = P-π/√π (1-π) / n

P = 507.4/860 = 0.59 (sample proportion)

n = 860 (sample size)

π = 0.55 (population porportion)

Zstat = 0.59-0.55/√0.55 (1-0.55) / 860

Zstat = 2.36

From Z table the probability of Z score of 2.36 is 0.9909

To calculate for P - value will then be

P = 1 - 0.9909

P = 0.0091