Sandra Broom manages the Tip-Top Fitness Club. She recently installed a machine

Question

Sandra Broom manages the Tip-Top Fitness Club. She recently installed a machine that is advertised to reduce the waists of individuals who exercise with it. To estimate the effectiveness of the machine, she closely monitored the measurements of 64 members of the club. For the period of the study, Sandra obtained the following statistics for the 64 differences: d bar = 12.5 cm and s_4 = 2.4 cm Use these to construct a 95 percent confidence interval for the mean difference in waist measurements for individuals that exercise with this machine for a period of lime comparable to the one in the study.

Explanation / Answer

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = dbar - z(alpha/2) * s / sqrt(n)              
Upper Bound = dbar + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
dbar = sample mean =    12.5          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    2.4          
n = sample size =    64          
              
Thus,              
Margin of Error E =    0.587989195          
Lower bound =    11.9120108          
Upper bound =    13.0879892          
              
Thus, the confidence interval is              
              
(   11.9120108   ,   13.0879892   ) [ANSWER]

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