ou may need to use the appropriate appendix table or technology to answer this question. Individuals filing federal income tax returns prior to March 31 received an average refund of $1,059. 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 H0 will support the researcher's contention. A) H0: ?= $1,059 Ha: ? ≠ $1,059 B) H0: ?< $1,059 Ha: ?≥ $1,059 C) H0: ? ≥ $1,059 Ha: ? < $1,059 D) H0: ?> $1,059 Ha: ? ≤ $1,059 E) H0: ?≤ $1,059 Ha: ? > $1,059 (b) For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of ? = $1,600may be assumed. What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) At ? = 0.05,what is your conclusion? Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059. Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059. Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059. Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
You may need to use the appropriate appendix table or technology to answer this question.
Individuals filing federal income tax returns prior to March 31 received an average refund of $1,059. 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
H0
will support the researcher's contention.
- A) H0: ?= $1,059 Ha: ? ≠ $1,059
- B) H0: ?< $1,059 Ha: ?≥ $1,059
- C) H0: ? ≥ $1,059 Ha: ? < $1,059
- D) H0: ?> $1,059 Ha: ? ≤ $1,059
- E) H0: ?≤ $1,059 Ha: ? > $1,059
(b)
For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of ? = $1,600may be assumed.
What is the test statistic? (Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(c)
At ? = 0.05,what is your conclusion?
- Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059.
- Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.
- Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059.
- Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.
(d)
Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses.
- H0: ?= $1,059 Ha: ? ≠ $1,059
- H0: ?< $1,059 Ha: ? ≥ $1,059
- H0: ?≥ $1,059 Ha: ? < $1,059
- H0: ?> $1,059 Ha: ? ≤ $1,059
- H0: ?≤ $1,059Ha: ? > $1,059
Find the value of the test statistic. (Round your answer to two decimal places.)
State the critical values for the rejection rule. (Use ? = 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic ≤ _____
test statistic ≥ _________
State your conclusion.
- Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059.
- Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.
- Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059.
- Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.
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