The number of successes and the sample size are given for a simple random sample from a population. Decide whetherusing the one-proportion z-interval procedure is appropriate.
-x = 2, n = 40
A)Not appropriate
B)Appropriate

Question

The number of successes and the sample size are given for a simple random sample from a population. Decide whetherusing the one-proportion z-interval procedure is appropriate.
-x = 2, n = 40 
A)Not appropriate
B)Appropriate

Quizplus · Accepted Answer

The one-proportion z-interval procedure requires that both np and n(1-p) are greater than 5, where n is the sample size and p is the sample proportion. Here, with x = 2 successes out of n = 40 trials, the sample proportion p = x/n = 2/40 = 0.05. Thus, np = 40*0.05 = 2 and n(1-p) = 40*0.95 = 38. Since np is not greater than 5, the procedure is not appropriate.

The Number of Successes and the Sample Size Are Given