Answered: For a sample of 400 individuals who…

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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For a sample of 400 individuals who filed a tax return between April 10th and 15th, 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)?

**Chapter 9: Hypothesis Testing for Mean Refund Differences**

According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,070 in 2018. 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. Hypothesis Development**

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 $ H_0 $ will support the researcher’s contention.

- $ H_0: \mu = $ [Select your answer]
- $ H_a: \mu < $ [Select your answer]

**b. Sample Analysis**

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 $ \sigma = \$1,600 $ may be assumed. What is the $ p $-value (to 4 decimals)?

[Input field for numerical answer]

**c. Conclusion Using a Significance Level**

Using $ \alpha = 0.05 $, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers?

- [Dropdown: Yes/No]

**d. Critical Value Approach**

Repeat the preceding hypothesis test using the critical value approach.

- Using $ \alpha = 0.05 $, what is the critical value for the test statistic (to 3 decimals)? Enter the negative value as a negative number.

[Input field for critical value]

- State the rejection rule: Reject $ H_0 $ if $ z $ is [Select your answer] the critical value.

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

- [Dropdown: Yes/No]

**Check My Work** (2 remaining)

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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