A 95 confidence interval for the mean price of textbooks at

A. 95% confidence interval for the mean price of textbooks at a university based on a random sample was ($59.06:$77.98). Assuming that nothing else changed, what would have been lie effect on the confidence interval if a larger sample size was used? Assume that the necessary conditions for finding a confidence interval hold. Choose the correct answer below. The confidence level would have been lower. The confidence interval would have been narrower. The confidence level would have been higher. The confidence interval would have been wider.

Solution

If a larger sample size was used, the standard error of the mean becomes lower, as

standard error = s / sqrt(n).

Thus, that will produce a NARROWER CONFIDENCE INTERVAL. [OPTION B]

[This is intuitive, because you have a better idea of the population, so you are more confident of a narrower interval.]