Question

Individuals filing federal income tax returns prior to March 31 received an average refund of $1066. 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. 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. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention.

H0: u is: greater than 1066, greater than or equal to 1066, equal to 1066, not equal to 1066, less than 1066, less than or equal to 1066

Ha: u is: greater than 1066, greater than or equal to 1066, equal to 1066, not equal to 1066, less than 1066, less than or equal to 1066

b. 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 a population standard deviation of o=$1600 may be assumed. What is the p-value? (to 4 decimals)?

c. using a=0.05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?

Answer the next 3 questions with using the critical value approach.

d. Using a= 0.05, what is the critical value for the test statistic? enter negative value as negative number.

State the rejection rule: Reject a=0.05 if z is: greater than, greater than or equal to, equal to, not equal to, less than, less than or equal to the critical value.

Answer 1

a) The Null and alternative hypothesis:

H₀ : is equal to 1066.

H_a: is less than 1066.

Test statistic: The z-statistic is computed as follows:

b)  The p-value is p = 0.0256.

c) since p = 0.0256 < 0.05  it is concluded that the null hypothesis is rejected.

We conclude that the population mean refund for last minute filers is less than the population mean refund for early filers.

ANS: Yes.

d) The critical value is -1.64.

Rejection rule: reject if z is less than the critical value.

  Since it is observed that z = -1.95 < −1.64, it is then concluded that the null hypothesis is rejected.

We conclude that the population mean refund for last minute filers is less than the population mean refund for early filers.

   ANS: Yes.