Question

Fourty-two sets of siblings who suffered from insomnia were recruited for a study on a new medication that could help them fall asleep faster. To support this claim, one sibling was given the medication and one was given a placebo. The average amount of time that it took the sibling on medication to fall asleep was 4.75 minutes with a standard deviation of 2 minutes, and the average amount of time that it took the sibling on placebo to fall asleep was 8 minutes with a standard deviation of the difference of 3 minutes. The average difference in minutes to fall asleep was 3.25 minutes with a standard deviation of the difference of 3 minutes. provide a confidence interval for the true mean difference in minutes to fall asleep between the siblings on the medication and those on the placebo. Interpret the interval in a sentence.

Answer 1

The 95% confidence interval for the true mean difference in minutes to fall asleep between the siblings on the medication and those on the placebo is between -4.35675 and -2.14325.

We are 95% confident that the true mean difference in minutes to fall asleep between the siblings on the medication and those on the placebo is between -4.35675 and -2.14325.

1	2
4.75	8	mean
2	3	std. dev.
42	42	n
	82	df
	-3.25000	difference (1 - 2)
	6.50000	pooled variance
	2.54951	pooled std. dev.
	0.55635	standard error of difference
	-4.35675	confidence interval 95.% lower
	-2.14325	confidence interval 95.% upper
	1.10675	margin of error