Question

In: Statistics and Probability

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,076....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,076. 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 : is ? Ha : is ?

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 = $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? Answer the next three questions using the critical value approach.

d. Using = .05, what is the critical value for the test statistic (to 3 decimals)? If your answer is negative use minus "-" sign.

e. State the rejection rule: Reject H0 if z is 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?

Solutions

Expert Solution

(a) H0: Null hypothesis: 1076

HA: Alternative hypothesis: < 1076

(b) n = sample size = 400

= sample mean = 930

= population SD = 1600

SE=/ = 1600/ = 80

Test statistic is:
Z = ( - )/SE

= (930 - 1076)/80 = - 1.825

One tail - left side test

Table of Area Under Standard Normal Curve gives area = 0.4664

So,

the p-value= 0.5 - 0.4664 = 0.0336

(c) Since p-value = 0.0336 is less than = 0.05, H0 is rejected.

Conclusion:

The population mean refund for "last minute" filers is less thn the population mean refund for early filers.

(d) = 0.05

From Table, critical value of Z = - 1.64

(e) Rejection region:

Reject H0 if Z is less than the critical value = - 1.64

(f) Since the calculated value of Z = - 1.825 is less than the critical value of Z = - 1.64, H0 is rejected, as already calculated.

Conclusion:

The population mean refund for "last minute" filers is less than the population mean refund for early filers.

orchestra answered 2 years ago
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