Question

An auto insurance company usually sends out its membership invitations to the residents in the city. They usually get back around 25% of the mailing list. The company wants to see the response rate for the future, they did a simulation using the sample size of 10, 40, 10 0.500. They did a simulation with the percentage of receiving a response is p=30%. For each sample size, 1000 mailing list was created and the histogram of the 1000 sample proportions was constructed. Answer questions below to explain how these histograms demonstrate what Central Limit Theorem says about sampling distribution for sample proportion. Bar re

Answer 1

Correct answer is- decreases

As sample size increases, the spread of the sampling distribution decreases.

Here = 0.25 p = Op = P(1-P) 400 1oo 500 LO 0.137 0.068 0.043 O. Olg op The more spread out a data distribution is the greater its standard deviation. Here, n increases standard deviation is decreasing Hence, as sample size increases, spread of the sampling distribution decreases.