The average length of a flight by regional airlines in the U

The average length of a flight by regional airlines in the United States has been reported as 464 miles. A random sample of 36 flights by regional airlines shows average flight length of 479.6 miles with a standard deviation of 42.8 miles. Does the sample information indicate that a flight time is usually more than 464 miles? Use a 2.5% significance level.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   464  
Ha:    u   >   464  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.025   ,      
alpha =    0.025          
zcrit =    +   1.959963985      
              
Getting the test statistic, as              
              
X = sample mean =    479.6          
uo = hypothesized mean =    464          
n = sample size =    36          
s = standard deviation =    42.8          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.186915888          
              
Also, the p value is              
              
p =    0.014374332          
              
As |z| > 1.95996, and P < 0.025, we   REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence that the flight time is usually more than 464 miles at 0.025 level. [CONCLUSION]