Question

Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):

Brand A: 34.36    31.26    37.36    28.52    33.14    32.74    34.34    34.33    27.95
Brand B: 41.08    38.22    39.59    38.82    36.24    37.73    35.03    39.22    34.13    34.33    34.98    29.64    40.60

Let μXμX represent the population mean for Brand B and let μYμY represent the population mean for Brand A. Find a 98% confidence interval for the difference μX−μYμX−μY. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

The 98% confidence interval is (_ , _)

Answer 1

Sample #1   ---->   1
mean of sample 1,    x̅1=   32.67
standard deviation of sample 1,   s1 =    3.002319936
size of sample 1,    n1=   9
      
Sample #2   ---->   2
mean of sample 2,    x̅2=   37.662
standard deviation of sample 2,   s2 =    2.45
size of sample 2,    n2=   13

α=0.02

t-critical value =    t α/2 =    2.624   (excel formula =t.inv(α/2,df)      
                  
                  
                  
std error , SE =    √(s1²/n1+s2²/n2) =    1.209          
margin of error, E = t*SE =    2.624   *   1.209   =   3.17
                  
difference of means = x̅1-x̅2 =    32.6667   -   37.662   =   -4.9956
confidence interval is                   
Interval Lower Limit = (x̅1-x̅2) - E =    -4.9956   -   3.173   =   -8.168
Interval Upper Limit = (x̅1-x̅2) + E =    -4.9956   -   3.173   =   -1.823