Question

For a new study conducted by a fitness magazine, 270 females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-February period. A second sample of 285 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 2387.2 calories daily with a standard deviation of 216. During the March-August period, participants consumed a mean of 2412.8 calories daily with a standard deviation of 255. 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 90% confidence interval for −μ1μ2, the difference between the mean daily calorie consumption μ1 of females in September-February and the mean daily calorie consumption μ2 of females in March-August. Then complete the table below.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.)

What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?

Answer 1

Solution:

Given that

n1= 270 sample size of female mean daily calorie consumption in September to February period.

n2= 285 sample size of female mean daily calorie consumption in March to August period.

sample mean of female mean daily calorie consumption in September to February period.

sample mean of female mean daily calorie consumption in March to August period.

s1 = 216 sample standard deviations of female mean daily calorie consumption in September to February period.

s2 = 255 sample standard deviations of female mean daily calorie consumption in March to August period.

. Level of significance

The 90% confidence interval for difference in mean   is

Here n1> 30 , n2> 30

Where

At

. From Z table

​

( -25.6 - 32.985812, -25.6+ 32.985812)

( -58.58581, 7.385812)

(-58.59, 7.39)

The lower limit of the 90% confidence interval is -58.59

Lower limit = -58.59

The upper limit of the 90% confidence interval is 7.39

Upper limit = 7.39