You are working for the IRS. One of the things the IRS does is to test if a retu

Question

You are working for the IRS. One of the things the IRS does is to test if a return is based on "real" numbers or "fake" numbers. "Fake" returns usually have the first digits of the numbers is about the same proportion. For example, if there are 99 numbers, then approximately 11 will start with 1, 11 with 2, .., 11 with 9. Note: No zeros are counted. "Real" returns, however, are known to be heavily weighted with digits which start with 1's and 2's. In a tax return, the starting digits of the numbers are: Determine whether these numbers are taken from a "real" return or a "fake" return. a. What is the null hypothesis? b. What is the alternative hypothesis? c. Enter the observed number of times a digit occurs in the return and the expected number of times that digit should occur into the X-squared goodness of fit applet. 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. f. Using a 90% confidence interval, should you accept or reject the null hypothesis?

Explanation / Answer

a) null hypothesis : -

observed values are of same proportion

b) alternate hypothesis

observed values are from different proportion

c)

d) df = r-1 = 8

e) p-value = P(X^2 > 55.09) = 0.0000

f)since p-value is less than 0.10

we reject the null hypothesis

Oi Ei (Oi-Ei)^2/Ei 1 32 11 40.09091 2 14 11 0.818182 3 2 11 7.363636 4 9 11 0.363636 5 4 11 4.454545 6 12 11 0.090909 7 10 11 0.090909 8 7 11 1.454545 9 9 11 0.363636 Sum 99 55.09091

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