For a new study conducted by a fitness magazine,

210

females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-February period. A second sample of

220

females was chosen independently of the first. For each of them, the mean daily calorie consumption was calculated for a March-August period. During the September-February period, participants consumed a mean of

2380.5

calories daily with a standard deviation of

204

. During the March-August period, participants consumed a mean of

2419.5

calories daily with a standard deviation of

282.5

. The population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample standard deviations, as the samples that were used to compute them were quite large. Construct a

95%

confidence interval for

12

, the difference between the mean daily calorie consumption

1

of females in September-February and the mean daily calorie consumption

2

of females in March-August. Then find the lower limit and upper limit of the

95%

confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If necessary, consult a list of formulas.)

question

lower limit

upper limit