Question

In a study related to IRS refunds, it was found that individuals filing their federal income tax returns before March 31, 2018, received an average refund of $1,065. If you were to perform a hypothesis test, what would be the null and alternative hypotheses to determine whether the population of "last-minute" filers receives a different average refund?

Answer 1

To determine if 'last-minute' tax filers receive a different average refund, the null hypothesis (H0) states the average refund is $1,065, while the alternative hypothesis (H1) suggests that the average refund is different from $1,065. A hypothesis test will help determine if there is statistically significant evidence to reject H0 in favor of H1.

Step-by-step explanation:

Hypothesis Testing for Average IRS Refunds of 'Last-Minute' Filers

To perform a hypothesis test to determine whether the population of "last-minute" filers receives a different average refund compared to those who filed before March 31, 2018, we would set up our null and alternative hypotheses as follows:

• Null hypothesis (H0): The average refund for last-minute filers is equal to $1,065, the average for early filers. In mathematical terms, this is H0: μ = $1,065.
• Alternative hypothesis (H1): The average refund for last-minute filers is not equal to $1,065. This hypothesis is bidirectional, indicating that the average could be higher or lower. Thus, in mathematical terms, this is H1: μ ≠ $1,065.

The test will then determine if there is enough evidence to reject the null hypothesis in favor of the alternative. This could be done using significance levels and calculating p-values compared against this determined level (often 0.05).