An investor is planning on buying a parking garage The profi

An investor is planning on buying a parking garage. The profitability of the project depends on the parking patterns of the potential customers at the garage. The investor assumes that 40% of the customers stay less than 1 hour, 20% will stay from 1 to 2 hours, 15% will stay from 2-4 hours, and 25% will stay more than 4 hours. In a random sample of the parking patterns at a nearby parking lot the following distribution was observed:

1-2 hrs

Test the investor\'s assumptions at the 5% level of significance.

Solution

Sign. Lvl.   0.05      
          
Doing an observed/expected value table,          
O   E   (O - E)^2/E  
100   80   5  
35   40   0.625  
25   30   0.833333333  
40   50   2  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    8.458333333      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      

chi^2(crit) =    7.814727903      
          
Also, the p value is          
          
p =    0.03743079      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence to reject the claimed distribution of the distributor. [CONCLUSION]