To apply Central Limit Theorem on sample proportions in One

To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement?

Solution

Answer to the question)

The conditon is : n*p > 10 & n*(1-p) > 10

.

1) 36*0.25 = 9 is not greater than 10

2) 48 * 0.80 = 38.4 > 10 & 48*(1-0.8) = 9.6 is not greater than 10

3) 99*0.90 = 89.1 > 10 & 99 * (1-0.9) = 9.9 is not greater than 10

4) 200*0.06 = 12 > 10& 200*(1-0.06) = 188 > 10

Thus the fourth option meets the requirement