A survey claims that 9 of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative, that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. What is the approximate value of the test statistic in this ?
A) -2.33
B) -1.86
C) -1.67
D) -0.14

Question

Quizplus · Accepted Answer

We are testing the null hypothesis that the proportion of doctors who recommend aspirin is 0.90 against the alternative that it is less than 0.90.

Under the null hypothesis, the sample proportion of doctors who recommend aspirin should follow a normal distribution with mean 0.90 and standard deviation sqrt(0.9*0.1/100) = 0.03.

The test statistic is calculated as 
(z = (p̂ - p) / sqrt(p(1-p)/n))
where p̂ is the sample proportion, p is the null hypothesis proportion, and n is the sample size.

Substituting the values, we get
z = (0.83 - 0.90) / 0.03
z = -2.33

Thus, the approximate value of the test statistic is -2.33, which corresponds to the critical value at a significance level of 0.05.

A Survey Claims That 9 of 10 Doctors Recommend Aspirin