True or False As the amount of confidence increases the required sample size should decrease Explain your answer?

Answer 1

I can examine this as a question of theory or real life: As a matter of theory, I will rephrase your question as follows: Does theoretical confidence interval of the mean (CI) of a sample, size n become larger as n is reduced? The answer is true. This is established from the sampling distribution of the mean. The sampling distribution is the probability distribution of the mean of a sample, size n. I will also consider the question as a matter of real life: If I take a sample from a population, size 50 and calculate the CI and take a smaller sample, say size 10, will I calculate a larger CI? If I use the standard deviation calculated from the sample, this is not necessarily true. The CI should be larger but I can't say in every case it will belarger. The standard deviation of the sample will vary from sample to sample. I hope this answers your question. You can find more information on confidence intervals at: http://onlinestatbook.com/chapter8/mean.html