Question

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):

Answer 1

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)