Question

a quality control inspector selects 12 bottles of apple juice at random from a single days production. the mean amount of apple juice in the bottles is 298.3 milliliters, and the 95% confidence interval for the true mean amount of juice dispensed per bottle is (296.4, 300.2). does this interval give the quality control inspector reason to believe that the mean amount of juice in todays bottles differs from 300 milliliters, as the juice label promises?
yes, since the sample mean of 298.3 ml is less than 300 ml.
yes, since nearly the entire confidence interval is less than the advertised value of 300 ml.
no, since the sample mean of 298.3 ml is in the confidence interval.
no, since the advertised value of 300 ml is in the confidence interval.

Explanation:

A 95% confidence interval for the true mean contains values we reasonably believe could be the true population mean. If the advertised value (300 ml) lies within this interval, we do not have sufficient evidence to conclude the true mean differs from 300 ml. Here, 300 is within (296.4, 300.2).

Answer:

No, since the advertised value of 300 ml is in the confidence interval.