Americans have a mean height of 175 cm Suppose a random samp

Americans have a mean height of 175 cm. Suppose a random sample of of 100 Americans taken this year shows a mean height of 174 cm. and we assume o=10 cm. Use the confidence interval approach to test (at significance level = 0.01) whether the population mean height of Americans has changed from 175 centimeters.   

Solution

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 =    0.005          
X = sample mean =    174          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    10          
n = sample size =    100          
              
Thus,              
              
Lower bound =    171.4241707          
Upper bound =    176.5758293          
              
Thus, the confidence interval is              
              
(   171.4241707   ,   176.5758293   ) [ANSWER, CONFIDENCE INTERVAL]

As this still includes 175 cm, there is no significant evidence that the population mean height of Americans has changed from 175 centimeters. [CONCLUSION]