AS a professional courtesy, physicians have traditionally provided health care f

Question

AS a professional courtesy, physicians have traditionally provided health care free of charge or at a reduced rate to other physicians and their families. In 1986, 94% of a sample of 1,000 physicians offered this professional courtesy. To assess the extent to which this practice has changed over the Years, The New England Journal Of Medicine conducted a survey of 2, 224 physicians of which 1, 957 currently offer free or reduced - rate health care to fellow physicians. Test statistic Z = p^cap _1 - p^cap _2/squarerootp^cap q^cap (1/n_1 + 1/n_2) With p^cap = x_1 + x_2/n_1 + n_2

Explanation / Answer

Hypothesis:
H0: P1 = P2
Ha: P1 P2

Data:

x1 = 94% *1000 = 940 , x2 = 1957,
n1 = 1000 , n2 = 2224 , p1 = =0.94 , p2 = 0.88

Test statistic:

p cap = (x1 + x2) / (n1 + n2)
= ( 940 + 1957)/(1000 + 2224)
= 0.8985
q cap = 0.1015
z = ( p1 - p2)/ sqrt(pcap * qcap * ( 1/n1+1/n2))
= (0.94 - 0.88) / sqrt ( 0.8985 * 0.1015 * ( 1/1000+ 1/2224))
= 5.2183

p value is calculated using z = 5.2183
p value = 0.00001.

we rejecct the null hypothesis.

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