Question

Individuals filing federal income tax returns prior to March 31 received an average refund of 1075. 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 Ho will support the researcher's contention.

Ho:  is - Select your answer -greater than or equal to 1,075 greater than 1,075 less than or equal to 1,075 less than 1,075 equal to 1,075 not equal to 1,075 Item 1
H∞:  is - Select your answer -greater than or equal to 1,075 greater than 1,075 less than or equal to 1,075 less than 1,075 equal to 1,075 not equal to 1,075 Item 2

b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was 930. Based on prior experience a population standard deviation of 1600 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 filers?
- Select your answer -YesNoItem 4

Answer the next three questions using the critical value approach.

d. Using .05, what is the critical value for the test statistic? Enter negative value as negative number.

State the rejection rule: Reject .05 if z is( - Select your answer -greater than or equal to greater than less than or equal to less than equal tonot equal toItem 6 the critical value.

Using .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?

Answer 1

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Answer:

a)
H0 :mu >= 1,075
Ha : mu < 1075

b)
x = 930 , s = 1600, n =400

z = ( x -mean) / (s/sqrt(n))
= ( 930 - 1075)/(1600/sqrt(400))
= -1.8125

p value = 0.0350

c)
yes,we can conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers.

d)
Critical value = -1.645

e)
Reject H0 if z<= -1.645

f)
yes