Suppose a sample of 49 paired differences that have been ran

Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of formula157.mml and a sample standard deviation of sd = 7. (a) Calculate a 95 percent confidence interval for µd = µ1 – µ2. (Round your answers to 2 decimal places.) Confidence interval = [ , ]

Solution

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    157          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    7          
n = sample size =    49          
              
Thus,              
Margin of Error E =    1.959963985          
Lower bound =    155.040036          
Upper bound =    158.959964          
              
Thus, the confidence interval is              
              
(   155.040036   ,   158.959964   ) [ANSWER]