A survey claims that 9 out 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.The value of the test statistic in this problem is approximately equal to:
A)−1.67
B)−2.33
C)−1.86
D)−0.14

Question

Quizplus · Accepted Answer

The test statistic for this problem is given by:

z = (p̂ - p) / √(𝑝(1−𝑝)/𝑛)

Where p̂ is the sample proportion, p is the hypothesized proportion (0.90) and n is the sample size (100).

Substituting the given values, we get:

z = (0.83 - 0.90) / √(0.9 x 0.1 / 100) = -2.33

Since the alternative hypothesis is that the actual proportion of doctors who recommend aspirin is less than 0.90, this is a one-tailed test with rejection region in the left tail.

Using a significance level of 0.05 and a one-tailed test, the critical value for the test statistic is -1.645. Since the calculated value of z is smaller than the critical value, we reject the null hypothesis and conclude that the actual proportion of doctors who recommend aspirin is less than 0.90.

Therefore, the correct answer is B.

A Survey Claims That 9 Out of 10 Doctors Recommend