Distribution of Digits in the Rational Number 22/7 The number 22/7 is similar to
ID: 3223549 • Letter: D
Question
Distribution of Digits in the Rational Number 22/7 The number 22/7 is similar to "pi" in the sense that they both require an infinite number of decimal places. However, 22/7 is a rational number because it can be expressed as the ratio of two integers, whereas "pi" cannot. When rational numbers such as 22/7 are expressed in decimal form, there is a pattern of repetition. In the decimal representation of 22/7, the first 100 digits occur with the frequencies described in the accompanying table. At the 0.05 significance level, test the claim that the digits are uniformly distributed.
Digit 0 1 2 3 4 5 6 7 8 9
Frequency 0 17 17 1 17 16 0 16 16 0
Explanation / Answer
null hypothesis: digits are uniformly distributed
alternate hypothesis: digits are not uniformly distributed
from abvoe chi stat =63.6
and degree of freedom =10-1=9
for above p vlaue =0.0000
as p vlaue is less then 0.05 level we reject null hypothesis and conclude that digits are not uniformly distributed
observed Expected Chi square Digit Probability O E=total*p =(O-E)^2/E 0 0.10 0.00 10.00 10.00 1 0.10 17.00 10.00 4.90 2 0.10 17.00 10.00 4.90 3 0.10 1.00 10.00 8.10 4 0.10 17.00 10.00 4.90 5 0.10 16.00 10.00 3.60 6 0.10 0.00 10.00 10.00 7 0.10 16.00 10.00 3.60 8 0.10 16.00 10.00 3.60 9 0.10 0.00 10.00 10.00 100 100 63.6000