A sample of 25 observations is taken to estimate a population proportion π.The sampling distribution of sample proportion p is:
A)not normal since n

Question

A sample of 25 observations is taken to estimate a population proportion π.The sampling distribution of sample proportion p is:
A)not normal since n < 30. 
B)approximately normal because Is always normally distributed. 
C)approximately normal if np ≥ 5 and n(1 - p)≥ 5. 
D)approximately normal if p approaches 0.50.

Quizplus · Accepted Answer

The sampling distribution of sample proportion p is approximately normal if np ≥ 5 and n(1-p) ≥ 5. In this case, we need to ensure that both np and n(1-p) are greater than or equal to 5. This condition ensures that the sample size is large enough to use the normal distribution as an approximation for the sampling distribution of the sample proportion. Since we do not have any information about the population proportion, option D is not a valid choice. Option A is incorrect because it is overly restrictive - the sample size of 25 is not necessarily too small to allow for the normal approximation. Option B is incorrect because it assumes that the normality of sampling distribution rests solely on the distribution of the population (which is incorrect).

A Sample of 25 Observations Is Taken to Estimate a Population