Question

Which should be larger: a 90\% confidence interval based on a sample of size n=50n=50 or a 95\% confidence interval based on a sample of size n=50n=50? Explain.

Answer 1

The 95% CI is wider than that of 90% CI.

I assume we are are dealingf with the Confidence interval for population mean. Since the sample size, n-50 is fairly large we can assume a normal distribution for sample mesan.

Hence the CI for the population mean is given by

where is the standard deviation and   is the Z-value obtained from standard normal curve.

Now since the same sample is used to estimate 90% and 95% CI, clearly from above the only value that changes is the Z-value. From the standard normal tables we can see that as reduces or as increases the value of Z statistic increases. It is beacuse as   reduces Z moves towards the tails of the standard normal curve.

The Z-value for 90% CI is 1.645 and for 95% is 1.96.

Hence the 95% CI is wider than that of 90% CI.