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)
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)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3458b95-5123-4489-b2c3-cf4b0d696559%2F1cff684e-c77e-4bb1-aad0-2bfa9032713e%2Ff2tjknr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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)
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