Concerning the sampling distribution of , what is the significance of the conditions np ≥ 5 and n(1 - p) ≥ 5?
A) It is impossible to make any inference on p using unless both these conditions are met.
B) The sampling distribution of will be approximately normal if both these conditions are met.
C) It is possible to use to estimate p only if one of these conditions is met.
D) The value of will be very close to p if and only if the sample size is large enough for both these conditions to be met.

Question

Concerning the sampling distribution of  , what is the significance of the conditions np ≥ 5 and n(1 - p) ≥ 5?
A) It is impossible to make any inference on p using unless both these conditions are met. 
B) The sampling distribution of will be approximately normal if both these conditions are met. 
C) It is possible to use to estimate p only if one of these conditions is met. 
D) The value of will be very close to p if and only if the sample size is large enough for both these conditions to be met.

Quizplus · Accepted Answer

The conditions np ≥ 5 and n(1-p) ≥ 5 ensure that the sampling distribution of the sample proportion will be approximately normal. This is important for making inferences about the population proportion p. If these conditions are not met, the distribution may be skewed or have other non-normal characteristics that could affect the accuracy of our statistical tests and confidence intervals. Therefore, it is important to check these conditions before using 11eb86f3_5f6c_25f8_883a_37e1fa58bc71_TB8195_11 to make any inference about p.

Concerning the Sampling Distribution of , What Is the Significance