A sample of 100 apparently normal adult males 25 years old h

A sample of 100 apparently normal adult males, 25 years old, had a mean systolic blood pressure of 125. If it is believed that the population standard deviation is 15, find:

1a. The 90 percent confidence interval for .

1b. The 95 percent confidence interval for .

Solution

If you mean confidence interval for the mean:

1a.

Note that              
              
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 =    0.05          
X = sample mean =    125          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    15          
n = sample size =    100          
              
Thus,              
              
Lower bound =    122.5327196          
Upper bound =    127.4672804          
              
Thus, the confidence interval is              
              
(   122.5327196   ,   127.4672804   ) [ANSWER]

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1b.

Note that              
              
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 =    125          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    15          
n = sample size =    100          
              
Thus,              
              
Lower bound =    122.060054          
Upper bound =    127.939946          
              
Thus, the confidence interval is              
              
(   122.060054   ,   127.939946   ) [ANSWER]