A quality control inspector selects 12 bottles of apple juice at random from a single day’s 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 today’s bottles differs from 300 milliliters, as the juice label promises?
Answer
A
Yes, since the sample mean of 298.3 ml is less than 300 ml.
B
Yes, since nearly the entire confidence interval is less than the advertised value of 300 ml.
C
No, since the sample mean of 298.3 ml is in the confidence interval.
D
No, since the advertised value of 300 ml is in the confidence interval.
Explanation
The 95% confidence interval for the true mean is 296.4 to 300.2 milliliters. Because the advertised amount, 300 milliliters, falls within this interval, the data do not provide strong evidence that the true mean differs from 300 milliliters. The sample mean being below 300 milliliters alone is not enough to establish a difference.
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