Question

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,063. 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.

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

σ = $1,600

may be assumed.

What is the test statistic? (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

B.

Find the value of the test statistic. (Round your answer to two decimal places.)

State the critical values for the rejection rule. (Use α = 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

Answer 1

a)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (910 - 1063)/(1600/sqrt(400))
z = -1.91

P-value Approach
P-value = 0.0561

b)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (910 - 1063)/(1600/sqrt(400))
z = -1.91

Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96