Individuals filing federal income tax returns prior to March 31 received an average refund of $1,055. 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: ? ≤ $1,055 Ha: ? > $1,055H0: ? > $1,055 Ha: ? ≤ $1,055 H0: ? ≥ $1,055 Ha: ? < $1,055H0: ? < $1,055 Ha: ? ≥ $1,055H0: ? = $1,055 Ha: ? ≠ $1,055 (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 test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) At ? = 0.05, what is your conclusion? Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,055.Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,055. Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,055.Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,055.

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Description: Individuals filing federal income tax returns prior to March 31 received an average refund of $1,055. 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Individuals filing federal income tax returns prior to March 31 received an average refund of $1,055. 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: ? ≤ $1,055
H_a: ? > $1,055H₀: ? > $1,055
H_a: ? ≤ $1,055 H₀: ? ≥ $1,055
H_a: ? < $1,055H₀: ? < $1,055
H_a: ? ≥ $1,055H₀: ? = $1,055
H_a: ? ≠ $1,055

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

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

p-value =

(c)

? = 0.05,

what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,055.Reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,055. Do not reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,055.Do not reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,055.

(d)

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses.

H₀: ? ≤ $1,055
H_a: ? > $1,055H₀: ? > $1,055
H_a: ? ≤ $1,055 H₀: ? ≥ $1,055
H_a: ? < $1,055H₀: ? < $1,055
H_a: ? ≥ $1,055H₀: ? = $1,055
H_a: ? ≠ $1,055

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

State the critical values for the rejection rule. (Use ? = 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≥

State your conclusion.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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