A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 100 doctors was chosen which resulted in 83 who indicate that they recommend this cough syrup. The test statistic in this problem is approximately:
A) -2.33
B) 2.33
C) -1.83
D) -1.99

Question

Quizplus · Accepted Answer

The test statistic is approximately -2.33. This is because the sample proportion is 83/100 = 0.83, which is less than the claimed proportion of 0.90. The standard error of the proportion is sqrt(0.90*0.10/100) = 0.03. Therefore, the test statistic is (0.83 - 0.90) / 0.03 = -2.33.

A Company Claims That 9 Out of 10 Doctors (I