Question

According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience it is assumed a population standard deviation of $16000. Develop an appropriate hypotheses test to evaluate the researchers claim. Use alpha= 0.05.

1. Establish the two hypotheses
2. Calculate the test statistic
3. Make a decision using the critical value approach
4. Make a decision using the p-value approach
5. What can you conclude about the researchers claim?

Answer 1

Solution :

= 1056

=910

=16000

n = 400

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 1056

Ha :     1056

Test statistic = z

= ( - ) / / n

= (910-1056) / 16000 / 400

= -0.18

Test statistic = z = -0.18

The critical value = -1.96 and 1.96

P-value = 2 * 0.4286 =0.8572

= 0.05  

P-value >

0.8572 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that