Question

Right to be Angry? Critical Thinking: He's angry, but is he right? The following excerpt is taken from a letter written by a corporation president and sent to the Associated Press: When you or anyone else attempts to tell me and my associates that 1223 persons account for our opinions and tastes here in America, I get mad as hell! How dare you! When you or anyone else tells me that 1223 people represent America; it is astounding and unfair and should be outlawed. The writer then goes on to claim that because the sample size of 1223 people represents 120 million people, his letter represents 98,000 people (120 million divided by 1223) who share the same views. Analyzing the Results Given that the sample size is 1223 and the degree of confidence is 95%, find the margin of error for the proportion. Assume that there is no prior knowledge about the value of that proportion. The writer of the letter is taking the position that a sample size of 1223 taken from a population of 120 million people is too small to be meaningful. Do you agree or disagree? Write a response that either supports or refutes the writer's position that the sample is too small. As you write your answer be sure to use the information from the chapter - this is not the time for what you think is right. Your text will give you the correct response and the reasons for this being the correct response.

Answer 1

The width of the confidence interval will be Critical z-score / sqrt(n)

= Critical Z-score for confidence level of 95% / sqrt(1223)

= 0.0563

Hence, Margin of Error = 1/2 * (Width of confidence interval) (since confidence interval is given by estimated mean +/- Margin of Error, width of the confidence interval = 2* Margin of Error)

= 0.028 ~ 3%

The writer's claim that the sample size is too small is invalid. Given the small margin of error of 3%, it is a reasonably sized sample. What matters more here is the method used for sampling. If all classes of the population were represented well in the sample using a sampling technique like stratified sampling or simple random sampling, the sample given should just do the job for us.