A regional airline has been selling seats based on the assum

A regional airline has been selling seats based on the assumption that the average passenger weighs no more than 180 pounds. A recent survey of n = 100 passengers gave a sample mean of 186 pounds with a sample standard deviation of 32 pounds. The research hypothesis is that the average weight of passengers exceeds the standard, and is given a normal test.

Solution

We assume a 0.05 level here, as the significance level is not indicated.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   180  
Ha:    u   >   180  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    186          
uo = hypothesized mean =    180          
n = sample size =    100          
s = standard deviation =    32          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.875          
              
Also, the p value is              
              
p =    0.030396362          
              
As P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the average weight of passengers exceeds the standard. [CONCLUSION]