Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves. At an "ice cream social", people were randomly given either a 17 fluid oz (503 mL) or a 34 fluid oz (1006 mL) bowl. They were then invited to scoop as much ice cream as they liked. Did the bowl size change the selected portion size? Here are the summary statistics

Small Bowl Large Bowl

Sample Size 36 32

Sample Mean 5.07 oz 6.58 oz

Sample Standard Deviation 1.84 oz 2.91 oz

(a) Construct a 95% confidence interval for the true difference in mean portion size of ice cream.

(b) What assumptions must be satisfied for the inference in part (a) to be valid?