Answer:
98% confidence interval for the difference μX−μY = [ 0.697 , 7.303 ] .
Step-by-step explanation:
We are give the data of Measurements of the sodium content in samples of two brands of chocolate bar (in grams) below;
Brand A : 34.36, 31.26, 37.36, 28.52, 33.14, 32.74, 34.34, 34.33, 29.95
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 
Also,  represent the population mean for Brand B and let
 represent the population mean for Brand B and let  represent the population mean for Brand A.
 represent the population mean for Brand A.
Since, we know nothing about the population standard deviation so the pivotal quantity used here for finding confidence interval is;
         P.Q. =  ~
 ~  
 
where,  = Sample mean for Brand B data = 36.9
 = Sample mean for Brand B data = 36.9
              = Sample mean for Brand A data = 32.9
 = Sample mean for Brand A data = 32.9
                = Sample size for Brand B data = 13
  = Sample size for Brand B data = 13
                = Sample size for Brand A data = 9
 = Sample size for Brand A data = 9
                =
 =  = 3.013
 = 3.013
Here,  and
 and  are sample variance of Brand B and Brand A data respectively.
 are sample variance of Brand B and Brand A data respectively.
So, 98% confidence interval for the difference μX−μY is given by;
P(-2.528 <  < 2.528) = 0.98
 < 2.528) = 0.98
P(-2.528 <  < 2.528) = 0.98
 < 2.528) = 0.98 
P(-2.528 *  <
 <  < 2.528 *
 < 2.528 *  ) = 0.98
 ) = 0.98
P( (Xbar - Ybar) - 2.528 *  <
 <  < (Xbar - Ybar) + 2.528 *
 < (Xbar - Ybar) + 2.528 *  ) = 0.98
 ) = 0.98
98% Confidence interval for μX−μY = 
[ (Xbar - Ybar) - 2.528 *  , (Xbar - Ybar) + 2.528 *
 , (Xbar - Ybar) + 2.528 *  ]
 ]
[  ,
 ,  ]
 ]
[ 0.697 , 7.303 ]
Therefore, 98% confidence interval for the difference μX−μY is [ 0.697 , 7.303 ] .