Question

The IRS reports it takes an average of 40 hours to understand, complete, and mail form 1040. The population standard deviation is equal to six hours. With the institution of email filing the IRS now believes completion time will change. A sample of 100 taxpayers revealed the mean time to file was 39.25 hours. At the 0.05 significance level, can we conclude that e-filing caused the time to file taxes to decrease from the 40 hour average? State the null and alternative hypothesis and the decision rule. Compute the p-value. Interpret your answer.

Answer 1

Solution :

= 40

= 39.25

=6

n = 100

This is the left tailed test .

The null and alternative hypothesis is

H0 :   = 40

Ha : < 40  

Test statistic = z

= ( - ) / / n

= (39.25 - 40) / 6/ 100

= -1.25

P (Z < -1.25) = 0.1056

P-value = 0.1056

= 0.05  

Critical value = -1.645

0.1056 >  0.05

Do not reject the null hypothesis .

There is insufficient evidence to conclude that e-filing caused the time to file taxes to decrease from the 40 hour average.