suppose a Fellowes survey of 1002 people who file tax returns showed that 48% of

Question

suppose a Fellowes survey of 1002 people who file tax returns showed that 48% of them file through an accountant or other tax professional. The IRS claims that less than one half of tax filers use an accountant or tax professional.

a. What null and alternative hypotheses would be used to test the IRS claim?

b. Calculate the test statistic would be used to test the claim, based on the existing sample data.

c. If we wanted to test the claim at the 0.01 level, what critical value would we compare to the above test statistic?

d. Based on these results, what decision would you make about the null hypothesis?

e. Based on these results, what would you conclude about the IRS claim?

Explanation / Answer

(a) Ho: p = 0.5 versus Ha: p < 0.5

(b) SE = {p (1 - p)/n} = (0.5 * (1 - 0.5)/1002) = 0.0158   

z = (p' - p)/SE =   (0.48 - 0.5)/0.0157956005901641 =    -1.2662

(c) = 0.01

Critical z- score = -2.3263

(d) Since -1.2662 > -2.3263 we fail to reject Ho

(e) The claim is not true.

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