Question

In: Statistics and Probability

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,064....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,064. 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 : M is ( ) H a : M is ( )

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 = $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? (Yes or No) Answer the next three questions using the critical value approach.

d. Using a= .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 H 0 if z is ( less than or,....) the critical value. f. Using a= .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? ( Yes or No)

Solutions

Expert Solution

population mean = $1,064

a) Hypothesis test:

therfore above test is left tailed.

b)

population standard deviation of = $1,600

sample mean (x) = $910

sample size n =400

Z- statistic:

=

= -154/80

=-1.925

P value = P(Z>1.925)

= 1-P(Z<1.925)

= 1-0.97257

= 0.0274

C) p value < 0.05 reject the H0.

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

d)

Z critical = 1.645

e)

so that

Reject the null hypothesis.

f)

Yes, this is sufficient evidence to conclude that 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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