In a sample of 100 households, the mean number of hours spent on social networking sites during the month of january was 50 hours. in a much larger study, the standard deviation was determined to be 6 hours. assume the population standard deviation is the same. what is the 98% confidence interval for the mean hours devoted to social networking in january?

The confidence interval for the population mean at a confidence level is . Here is the sample mean, is the critical value such that , and , where in turn is the assumed population standard deviation and is the sample size.

First find the critical value. By the empirical rule, you might already know that about 95% of a normal distribution lies within two standard deviations of the mean, and that about 99.7% lies within three standard deviations, so you can expect to lie somewhere between 2 and 3. To be more precise, you can consult a z-score table to find that .

Plug in everything you know and you find that the 98% confidence interval is