Question

number 2

1). In order to estimate the proportion of taxpayers who underpay Federal Income Tax, a sample of 1000 tax filings is inspected, and it is found that in 641 cases there were underpayments. Compute 99% confidence intervals for the proportion, p, of taxpayers who underpay (give each interval in both forms, estimate error margin, and (Lower, Upper)). 2). Use the data in problem 1 to test He: p= .6 vs H: 7.6. Find: : P-value

Answer 1

The sample proportion of under payments p = 641 $\div$ 1000 = 0.641

The standard deviation of the sample proportion is found as follows

p(1-p) 0.641 x (1 – 0.641) 1000

$\sigma$p = 0.0152

The 99% confidence interval for the proportion p of taxpayers who underpay is given as

p+2.580

0.641 +2.58 * 0.0152

( 0.6802 , 0.6018)

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2)

To test the hypothesis

=Z - a

p = sample proportion = 0.641

$\pi$ = population proportion = 0.6

σp  = 0.0152

Z 0.641 - 0.6 0.0152

Z = 2.7

Looking at the Z score table for a value of 2.7

P value = 0.99653

The P value is greater than 99% hence the null hypothesis cannot be rejected.