A program for generating random numbers on a computer is to be tested. The progr

Question

A program for generating random numbers on a computer is to be tested. The program is instructed to generate 100 single-digit integers between 0 and 9. The frequencies of the observed integers were as follows. At the .05 level of significance, is there sufficient reason to believe that the integers are not being generated uniformly?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
< p <  

Explanation / Answer

If they are uniform, ideally there are 10 of each digit.

a)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
0   7   0  
1   9   7.111111111  
2   9   5.444444444  
3   13   7.692307692  
4   12   5.333333333  
5   7   0.571428571  
6   6   0  
7   9   0.444444444  
8   4   4  
9   24   9.375  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    39.9720696   [ANSWER, TEST STATISTIC]

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

b)  
          
As df = a - 1,           
          
a =    10      
df = a - 1 =    9      
          
Hence, the p value is          
  
0 < P < 0.005 [ANSWER]
      
[The exact answer using technology is p =    7.68757*10^-6. Please use the bounds you usually use in class. Thanks!]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.