For a test of hypothesis on p, it is safe to assume if:
A) np0 ≤ 5 and n(1-p0) ≤ 5.
B) np0 ≤ 5 and n(1- p0) ≥ 5.
C) np0 ≥ 5 and n(1-p0) ≥ 5.
D) np0 ≥ 3 and n(1-p0) ≥ 3.

Question

For a test of hypothesis on p, it is safe to assume  if:
A) np0 ≤ 5 and n(1-p0) ≤ 5. 
B) np0 ≤ 5 and n(1- p0) ≥ 5. 
C) np0 ≥ 5 and n(1-p0) ≥ 5. 
D) np0 ≥ 3 and n(1-p0) ≥ 3.

Quizplus · Accepted Answer

According to the normal approximation of the binomial distribution, it is safe to assume 11eb86f3_5f64_3693_883a_09a8d0779587_TB8195_11 if both np and n(1-p) are greater than or equal to 5. Hence, the best choice is C, where np0 ≥ 5 and n(1-p0) ≥ 5. This ensures that the sample size is large enough for the normal approximation to hold. The other options are not safe assumptions as they do not satisfy both the conditions for the normal approximation.

For a Test of Hypothesis on P, It Is Safe