Confidence Interval for a Mean Difference

A researcher conducts an experiment in which $10$ randomly selected students are invited to eat dinner at a restaurant on two different evenings. On one evening each student receives a regular-size plate and on the other they receive a large-size plate.

On each occasion, the students are allowed to choose as much food as they want from a buffet. Once the students have made their selection, their plates are weighed.

The table below shows how much food (in grams) each student chose when they were a given a regular-size plate $(X)$ and when they were given a large-size plate $(Y)$ :

Student	1	2	3	4	5	6	7	8	9	10
$X:\,\text{Regular}$	347	427	383	373	421	317	305	426	311	374
$Y:\,\text{Large}$	293	472	450	386	474	356	357	443	346	387

You may assume that the amount of food eaten for either plate size is normally distributed.

Define $D=Y-X$ and construct a $92\%$ confidence interval for the population mean difference $\mu_D$ . Round your answers to $3$ decimal places.

$CI_{\mu_D,\,92\%}=\,($

$,\,\,\,$

$)$

8. Testing for Differences in Means and Proportions: Paired Samples t-test

Confidence Interval for a Mean Difference