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 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

Let μX represent the population mean for Brand B and let μY represent the population mean for Brand A.

Find a 98% confidence interval for the difference μX−μY. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

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 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 A data = 32.9

               = Sample size for Brand B data = 13

              = Sample size for Brand A data = 9

              = = 3.013

Here, and 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

P(-2.528 < < 2.528) = 0.98

P(-2.528 * < < 2.528 * ) = 0.98

P( (Xbar - Ybar) - 2.528 * < < (Xbar - Ybar) + 2.528 * ) = 0.98

98% Confidence interval for μX−μY =

[ (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 ] .