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Individuals filing federal income tax returns prior to March 31 received an average refund of $1,079. 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 Ho will support the researcher's contention. Ho:H is greater than or equal to 1,079 Ha: u is less than 1,079 b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $920. Based on prior experience a population standard deviation of o = $1,800 may be assumed. What is the p-value (to 4 decimals)? .0392 c. Using a = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers? Yes 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 o if z is less than or equal to 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?

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,079. 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 Ho will support the researcher's contention. Ho:H is greater than or equal to 1,079 Ha: u is less than 1,079 b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $920. Based on prior experience a population standard deviation of o = $1,800 may be assumed. What is the p-value (to 4 decimals)? .0392 c. Using a = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers? Yes 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 o if z is less than or equal to 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?

MATLAB: An Introduction with Applications
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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## Statistical Analysis of Tax Return Timing and Refund Amounts ### Context Individuals filing federal income tax returns prior to March 31 received an average refund of $1,079. This analysis considers "last-minute" filers who submit during the last five days of the income tax period, typically April 10 to April 15. ### Research Hypothesis A researcher suggests that individuals who file during the last five days receive lower refunds than early filers. **Hypotheses:** - \( H_0: \mu \) is **greater than or equal to 1,079** (null hypothesis) - \( H_a: \mu \) is **less than 1,079** (alternative hypothesis) ### Sample Data - Number of individuals: 400 - Sample mean refund: $920 - Population standard deviation (\( \sigma \)): $1,800 ### Statistical Testing #### Part b - **Objective:** Calculate the p-value (to 4 decimals). - **Result:** (incorrect entry) .0392 #### Part c - **Objective:** Determine if the population mean refund for "last-minute" filers is less than that for early filers using \( \alpha = 0.05 \). - **Conclusion:** Yes ### Critical Value Approach #### Part d - **Objective:** Identify the critical value for the test statistic (to 3 decimals) with \( \alpha = 0.05 \). - **Response:** (input required) #### Part e - **Objective:** Establish the rejection rule. - **Rule:** Reject \( H_0 \) if \( z \) is **less than or equal to** the critical value. #### Part f - **Objective:** Reaffirm conclusion based on critical value. - **Conclusion:** Yes ### Summary This analysis evaluates the hypothesis that "last-minute" filers receive smaller refunds than early filers, using both p-value and critical value approaches to support conclusions. Complete calculations are necessary for accuracy.
Transcribed Image Text:## Statistical Analysis of Tax Return Timing and Refund Amounts ### Context Individuals filing federal income tax returns prior to March 31 received an average refund of $1,079. This analysis considers "last-minute" filers who submit during the last five days of the income tax period, typically April 10 to April 15. ### Research Hypothesis A researcher suggests that individuals who file during the last five days receive lower refunds than early filers. **Hypotheses:** - \( H_0: \mu \) is **greater than or equal to 1,079** (null hypothesis) - \( H_a: \mu \) is **less than 1,079** (alternative hypothesis) ### Sample Data - Number of individuals: 400 - Sample mean refund: $920 - Population standard deviation (\( \sigma \)): $1,800 ### Statistical Testing #### Part b - **Objective:** Calculate the p-value (to 4 decimals). - **Result:** (incorrect entry) .0392 #### Part c - **Objective:** Determine if the population mean refund for "last-minute" filers is less than that for early filers using \( \alpha = 0.05 \). - **Conclusion:** Yes ### Critical Value Approach #### Part d - **Objective:** Identify the critical value for the test statistic (to 3 decimals) with \( \alpha = 0.05 \). - **Response:** (input required) #### Part e - **Objective:** Establish the rejection rule. - **Rule:** Reject \( H_0 \) if \( z \) is **less than or equal to** the critical value. #### Part f - **Objective:** Reaffirm conclusion based on critical value. - **Conclusion:** Yes ### Summary This analysis evaluates the hypothesis that "last-minute" filers receive smaller refunds than early filers, using both p-value and critical value approaches to support conclusions. Complete calculations are necessary for accuracy.
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