1.Computers are used to generate pseudo-random numbers x where 0 < x < 1. We wan
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Question
1.Computers are used to generate pseudo-random numbers x where 0 < x < 1. We want to test whether the computer generated numbers are evenly distributed according to their first digit, i.e. by .0xxx, .1xxx, .2xxx, …, .9xxx. For a series of 100 random numbers, the starting digits of the x’s are:
Determine whether these x’s can pass for a random number series.
a.What is the null hypothesis?
b.What is the alternative hypothesis?
c.Enter the observed number of times a digit occurs in the pseudo-random series and the expected number of times that digit should occur into the X-squared goodness of fit applet. (Link below)
http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/goodness.htm
d.What is the number of degrees of freedom?
e.What is the p-value? Provide a screen shot of your answer. (PLEASE DO NOT ANSWER IF YOU CANNOT PROVIDE A SCREEN SHOT. THANKS IN ADVANCE)
f.Using a 90% confidence interval, should you accept or reject the null hypothesis?
Explanation / Answer
Ans:
Chi square test for Goodness of fit:
a)H0:x’s can pass for a random number series.
b)Ha:x’s can not pass for a random number series.
c)
Calculated Chi square score=8.8
d)Degree of freedom=10-1=9
e)p-value=CHIDIST(8.8,9)=0.4559
f)Significance level=1-0.9=0.1
As,p-value>0.1,we fail to reject null hypothesis.
There is sufficient evidence to suggest that x’s can pass for a random number series.
1st digit Observed(O) Expected(E) (O-E)^2/E 0 9 10 0.1 1 14 10 1.6 2 9 10 0.1 3 9 10 0.1 4 5 10 2.5 5 13 10 0.9 6 15 10 2.5 7 9 10 0.1 8 10 10 0 9 7 10 0.9 Total 100 100 8.8Related Questions
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