According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,072 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. 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: 4 is less than or equal to 1,072 H: u is- Select your answer - 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 = $1,600 may be assumed. What is the p-value (to 4 decimals)? c. Using a = 0.05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? - Select your answer - : d. Repeat the preceding hypothesis test using the critical value approach. Using a = 0.05, what is the critical value for the test statistic (to 3 decimals)? Enter negative value as negative number. State the rejection rule: Reject Ho if z is Select your answer- e 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? - Select your answer -
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,072 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.** 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.
- \( H_0 \): \( \mu \) is less than or equal to 1,072
- \( H_a \): \( \mu \) is [Select your answer]
**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 \(\sigma = \$1,600\) may be assumed. What is the *p*-value (to 4 decimals)?
- [Textbox for answer]
**c.** 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?
- [Select your answer]
**d.** 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 negative value as negative number.
- [Textbox for answer]
State the rejection rule: Reject \( H_0 \) if [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?
- [Select your answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d8ced1e-c405-49cc-9707-ee99115bb45e%2Fbc87c46c-f288-4413-9f68-2d4c5d57235e%2Fanm9ra_processed.jpeg&w=3840&q=75)
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