The Pennsylvania Daily Number is a state lottery game in which the state con- st

Question

The Pennsylvania Daily Number is a state lottery game in which the state con- structs a three-digit number by drawing a digit between 0 and 9 from each of three different containers. If the digits drawn, in order, were 3, 6, and 3, for exam- ple, then the daily number would be 363. In this example, we focus only on draws from the first container. I numbers are randomly selected, each value between0 and 9 would be equally likely to occur. This leads to the following null hypothesis: Ho:p = 10 for each of the 10 possible digits in first container riate hupothesis ferform an offropriate hyotasis test to dacide wheter to rerect or to réject or Hois talse to retain Ho, when Ha: Hoi fase.

Explanation / Answer

As significance level is not given, we assume it is 0.05.

There are 500 draws, so we expect 500/10= 50 draws for each digit.

Doing an observed/expected value table,          

          

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    6.04      
          
As df = a - 1,           
          
a =    10      
df = a - 1 =    9      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    16.9189776      
          
Also, the p value is          
          
p =    0.735908337      
          
As chi^2 > 16.91898, and P > 0.05 (very large P), we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that the null hypothesis is false. [CONCLUSION]

O E (O - E)^2/E 47 50 0.18 50 50 0 55 50 0.5 46 50 0.32 53 50 0.18 39 50 2.42 55 50 0.5 55 50 0.5 44 50 0.72 56 50 0.72

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