Dark Chocolate for Good Health

A study¹examines chocolate's effects on blood vessel function in healthy people. In the randomized, double-blind, placebo-controlled study,11

people received46

grams (1.6

ounces) of dark chocolate (which is naturally flavonoid-rich) every day for two weeks, while a control group of10

people received a placebo consisting of dark chocolate with low flavonoid content. Participants had their vascular health measured (by means of flow-mediated dilation) before and after the two-week study. The increase over the two-week period was measured, with larger numbers indicating greater vascular health. For the group getting the good dark chocolate, the mean increase was1.3

with a standard deviation of2.32

, while the control group had a mean change of-

0.96

with a standard deviation of1.58

.

¹Engler, M., et. al., ''Flavonoid-rich dark chocolate improves endothelial function and increases plasma epicatechin concentrations in healthy adults,"Journal of the American College of Nutrition, 2004 Jun; 23(3): 197-204.

(a) Find a95%

confidence interval for the difference in means between the two groups

C

-

N

, where

C

represents the mean increase in flow-mediated dilation for people eating dark chocolate every day and

N

represents the mean increase in flow-mediated dilation for people eating a dark chocolate substitute each day. You may assume that neither sample shows significant departures from normality.

Round your answers to two decimal places.

The95%

confidence interval is

to

.

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(b) Is it plausible that there is ''no difference" between the two kinds of chocolate?

Yes

No