A random sample of n 15 men between 30 and 39 years old is

A random sample of n = 15 men between 30 and 39 years old is asked to do as many situps as they can in one minute The table below reports the descriptive statistics for this study The investigators would like to construct a 98% confidence interval for the true number of situps men in this age group can complete in 1 minute. The margin of error is: The corresponding 98% confidence interval for the true population mean is:

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    41.8          
t(alpha/2) = critical t for the confidence interval =    2.624494068          
s = sample standard deviation =    12.2          
n = sample size =    15          
df = n - 1 =    14          
Thus,              
              
Lower bound =    33.53277426          
Upper bound =    50.06722574          
              
Thus, the confidence interval is              
              
(   33.53277426   ,   50.06722574   ) [ANSWER, PART B]

Also,

MArgin of error = (upper-lower)/2 = 8.267225744 [ANSWER, MARGIN OF ERROR, PART A]