Carlos is analyzing the results of an experiment in which he is comparing the difference in weight gain by experimental mice after feeding them two different foods for one month. The difference in the mean weight gain is 0.6 grams. He has calculated the standard deviation of the difference in sample means as 0.305. What is the 68% confidence interval for the population mean difference?

between -0.6 and +0.6
between -1.2 and +1.2
between -0.305 and +0.305
between -0.610 and +0.610

Question

Carlos is analyzing the results of an experiment in which he is comparing the difference in weight gain by experimental mice after feeding them two different foods for one month. The difference in the mean weight gain is 0.6 grams. He has calculated the standard deviation of the difference in sample means as 0.305. What is the 68% confidence interval for the population mean difference?

between -0.6 and +0.6
between -1.2 and +1.2
between -0.305 and +0.305
between -0.610 and +0.610

anonymous · Answer

Recall the empirical rule: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule This rule says that $68\%$ of the distribution falls within one standard deviation of the mean. The endpoints of the $68\%$ confidence interval must then be the mean plus or minus the standard deviation.