4) Based on a random sample of 100 students at Community College, a 95% confidence interval for μ, the mean age of all students at Community College, is 21

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4) Based on a random sample of 100 students at Community College, a 95% confidence interval for μ, the mean age of all students at Community College, is 21.2 years to 26.6 years (21.2 < µ < 26.6). On the basis of this information, decide whether you agree or disagree with each of the following statements. Explain how you decide.

a) According to the confidence interval, the mean age of all students at Community College cannot possibly be 23.1 years.

b) The 99% confidence interval based on the sample taken above will give a smaller margin of error in the estimate of μ.

c) If the sample size is decreased to 40, the 95% confidence interval has a larger margin of error than the one obtained above.