Suppose we have two binomial populations where the true proportion of success is .2 for the first population and .3 for the second population.We take an SRS of size 4 from the first population,and the number of successes is 3.We take an SRS of size 400 from the second population,and the number of successes is 200.Why should be closer to .3?
A)Because the sample size is large
B)Because of nonresponse bias
C)Because .3 is close to .5
D)None of the above

Question

Suppose we have two binomial populations where the true proportion of success is .2 for the first population and .3 for the second population.We take an SRS of size 4 from the first population,and the number of successes is 3.We take an SRS of size 400 from the second population,and the number of successes is 200.Why should  be closer to .3?
A)Because the sample size is large 
B)Because of nonresponse bias 
C)Because .3 is close to .5 
D)None of the above

Quizplus · Accepted Answer

The sample size from the second population is much larger than the sample size from the first population. According to the law of large numbers, as the sample size increases, the sample proportion gets closer to the true population proportion. Therefore, the sample proportion from the second population, which has a larger sample size, is more representative of the true population proportion of .3.

Suppose We Have Two Binomial Populations Where the True Proportion