Individuals filing federal income tax returns prior to March 31 received an aver
ID: 2934858 • Letter: I
Question
Individuals filing federal income tax returns prior to March 31 received an average refund of $1,074. 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.
H 0: is Selectgreater than or equal to 1,074greater than 1,074less than or equal to 1,074less than 1,074equal to 1,074not equal to 1,074Item 1
H a: is Selectgreater than or equal to 1,074greater than 1,074less than or equal to 1,074less than 1,074equal to 1,074not equal to 1,074Item 2
b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $940. Based on prior experience a population standard deviation of = $1,600 may be assumed. What is the p-value (to 4 decimals)?
c. Using = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers?
SelectYesNoItem 4
Answer the next three questions using the critical value approach.
d. Using = .05, what is the critical value for the test statistic?
e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the critical value.
f. Using = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?
SelectYesNoItem 7
Explanation / Answer
a)
H0: mu greater than or equal to 1,074
H1: mu less than 1,074
b)
Test statistics, z = (940 - 1074)/(1600/sqrt(400)) = -1.675 = 1.675
p-value = 0.047
c)
As p-value is less than the significance level of 0.05
Hence we can conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers i.e. Yes
d)
Critical value = -1.65 = 1.65
e)
Reject H0 if z is greater than the critical value
f)
Hence we can conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers i.e. Yes