In: Statistics and Probability
In a comparison of two different weight-loss programs, obese participants were randomly assigned to one of two groups: (1) the soy group, a low-calorie group that ate only soy-based proteins, or (2) the traditional group, a low-calorie group that received 2/3 of their protein from animal products and 1/3 from plant products. One of the dependent measures collected was the amount of body fat loss as a percentage of initial body weight.
Summary data from each group based on this variable are listed below:
Soy group (treat this as μ1): N = 6, Mean = 2.3, Variance = 0.3
Traditional group (treat this as μ2): N = 6, Mean = 1.223, Variance = 0.251
Calculate the 95% confidence interval.
List the LOWER BOUND (Round to the nearest 2 decimal places):
List the UPPER BOUND (Round to the nearest 2 decimal places):
mean of sample 1, x̅1= 2.3000
vaiance,s1²==0.3
size of sample 1, n1= 6
mean of sample 2, x̅2= 1.223
variance of sample 2, s2² = 0.251
size of sample 2, n2= 6
difference in sample means = x̅1-x̅2 =
1.0770
std error , SE = √(s1²/n1+s2²/n2) =
0.3030
DF = min(n1-1 , n2-1 )= 5
t-critical value = t α/2 = 2.5706 (excel formula =t.inv(α/2,df)
margin of error, E = t*SE = 0.779
difference of means = x̅1-x̅2 =
1.0770
confidence interval is
Interval Lower bound= (x̅1-x̅2) - E =
0.30
Interval Upper bound= (x̅1-x̅2) + E =
1.86
(if above get wrong, also try this, (0.39,1.76)