A pilot claims that average flight times from Charlotte to M

A pilot claims that average flight times from Charlotte to Miami are not more than 90 minutes. In a random sample of 35 such flights, the average time is 94 minutes with a standard deviation of 9 minutes. Assuming standard deviation of all such flights is 8 minutes, test the claim at the 1% level of significance.

State null and alternative hypotheses:

Determine distribution of test statistic and compute its value:

Construct the rejection region:

Make your decision:

State your conclusion:

Compute the p-value (observed level of significance) for this test:

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   90  
Ha:    u   >   90   [ANSWER]

********************

b)

Here, as n > 30, we use z distribution. [ANSWER]
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    94          
uo = hypothesized mean =    90          
n = sample size =    35          
s = standard deviation =    9          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.629368792   [ANSWER, TEST STATISTIC]

*****************************          

c)

Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      

Thus, Reject Ho if z > 2.326. [ANSWER]

*********************

d)

As z > 2.326, we Reject Ho.   [ANSWER]

***********************

e)

Thus, there is significant evidence that the average flight times from Charlotte to Miami are more than 90 minutes. [CONCLUSION]

**********************

f)              

Also, the p value is, as this is left tailed,
              
p =    0.004277177   [ANSWER]