Question

A regional office of the IRS randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being too lenient with persons whose returns are being audited. For a simple random sample of 30 of the returns audited by Mr. Jones last year, an average of $322 in extra taxes was collected, with a standard deviation of $90. Based on this information do the suspicions regarding Mr. Jones appear to be justified at significance level of 0.01? (Using Classical Approach)

Answer 1

Solution :

= 356

=322

=90

n = 30

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 356

Ha :     356

Test statistic = t

= ( - ) / / n

= (322 -356) / 90 / 30

= −2.069

Test statistic = t = −2.069

P-value =0.0475

= 0.01

P-value <

0.0475 ≥ 0.01

Do not reject the null hypothesis .

There is insufficient evidence to suggest that