An article presents a study of the effect of the subbase thi

An article presents a study of the effect of the subbase thickness on the amount of surface deflection caused by aircraft landing on an airport runway. In six applications of a 156 kN load on a runway with a subbasc thickness of 410 mm, the average surface deflection was 3.25 mm with a standard deviation of 0.50 mm. Can you conclude that the mean surface deflection is greater than 3 mm? Round the test statistic to four decimal places. Since the P-value is 0.1376, we cannot conclude that the mean surface deflection is greater than 3 mm. Can you conclude that the mean surface deflection is greater than 2.5 mm? Round the test statistic to four decimal places. Since the P-value is conclude that the mean surface deflection is greater than 2.5 mm.

Solution

Part 1 out of 2:

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   3  
Ha:    u   >   3  
              
As we can see, this is a    right   tailed test.      
              
df = n - 1 =    5          
              
Getting the test statistic, as              
              
X = sample mean =    3.25          
uo = hypothesized mean =    3          
n = sample size =    6          
s = standard deviation =    0.5          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.224744871          
              
Also, the p value is              
              
p =    0.137609866 [ANSWER, P VALUE]          
              
As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          
      
Thus, we CANNOT [ANSWER] conclude that the mean surface deflection is greater than 3 mm.

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Part 2 out of 2:

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   2.5  
Ha:    u   >   2.5  
              
As we can see, this is a    right   tailed test.      
              
df = n - 1 =    5          
              
Getting the test statistic, as              
              
X = sample mean =    3.25          
uo = hypothesized mean =    2.5          
n = sample size =    6          
s = standard deviation =    0.5          
              
Thus, t = (X - uo) * sqrt(n) / s =    3.674234614          
              
Also, the p value is              
              
p =    0.007189865   [ANSWER, P VALUE]      
              
As P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Thus, we CAN [ANSWER] conclude that the mean surface deflection is greater than 2.50 mm.