Answer to Question #316050 in Statistics and Probability for Seemu

Question

A 95% confidence interval is smaller than 99% confidence interval. State whether the given statement is true or false give reason in support of answer

Answer 1

The confidence interval can be found the following way

$x\in (a-Cr*{\frac s {\sqrt n}},a+Cr*{\frac s {\sqrt n}})$ , where x - population mean, a - sample mean, Cr - critical value s - population or sample standard deviation, n - sample size

The only thing that relate to the confidence level is Cr. So, the point is to determine how increasing of the confidence level affects critical value. Critical value is such value that a random variable that representing that critical value(it can be z-score, Student's distribution etc) will take value inside interval (-Cr, Cr) with $\alpha$-probability. For any distribution the greater probability, the wider interval. So, increasing of the confidence level always leads to the increasing of the confidence interval, which means 95% confidence interval is indeed smaller than 99%