A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in

kg

) by the people who take them.

The dietician tracks the total weight gain (in

kg

) over a year of a random sample of

14

people taking Ripped and a random sample of

13

people taking Gainz. (These samples are chosen independently.) For the people taking Ripped, their sample mean is

10.89

with a sample variance of

5.60

. For the people taking Gainz, their sample mean is

9.74

with a sample variance of

0.62

.

Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the

0.05

level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the weights gained by people taking Gainz?

Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

(a)	State the null hypothesis H0 and the alternate hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	(Choose one)
(c)	Find the value of the test statistic. (Round to three or more decimal places.)
(d)	Find the two critical values. (Round to three or more decimal places.)
and
(e)	At the 0.05 level of significance, can the dietician conclude that there is a difference between the mean weight gained by people taking Ripped and the mean weight gained by people taking Gainz?
Yes No