Math Problem Statement
Question content area top
Part 1
In a random sample of
100100
audited estate tax returns, it was determined that the mean amount of additional tax owed was
$34753475
with a standard deviation of
$25072507.
Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.
Question content area bottom
Part 1
Find and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Select the correct choice below and fill in the answer boxes to complete your choice.
(Use ascending order. Round to the nearest dollar as needed.)
A.
One can be 90% confident that the mean additional tax owed is between
$enter your response here
and
$enter your response here.
B.
90% of taxes owed for estate tax returns are between
$enter your response here
and
$enter your response here.
C.
There is a 90% probability that the mean additional tax owed is between
$enter your response here
and
$enter your response here.
Solution
To construct a 90% confidence interval for the mean additional tax owed for estate tax returns, we can use the following formula for the confidence interval (CI):
Where:
- (sample mean)
- (sample standard deviation)
- (sample size)
- is the z-score corresponding to the desired confidence level.
Step 1: Find the z-score for a 90% confidence level.
The z-score for a 90% confidence level (using a z-table or calculator) is approximately .
Step 2: Calculate the standard error (SE).
Step 3: Calculate the margin of error (ME).
Step 4: Construct the confidence interval.
Final Confidence Interval
Rounding to the nearest dollar:
- Lower limit: $30,629,538
- Upper limit: $38,877,412
Interpretation
The correct interpretation is: A. One can be 90% confident that the mean additional tax owed is between $30,629,538 and $38,877,412.
Summary
The 90% confidence interval for the mean additional amount of tax owed for estate tax returns is to .
Do you want details on any specific part or have any questions? Here are some follow-up questions you might consider:
- How would the confidence interval change with a larger sample size?
- What are the implications of the standard deviation in this context?
- How do you interpret the concept of confidence intervals in general?
- What factors could affect the accuracy of this confidence interval?
- How would you approach constructing a confidence interval for a different confidence level (e.g., 95%)?
Tip: Always check the underlying assumptions of normality and sample size when constructing confidence intervals.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Sampling Distributions
Formulas
CI = x̄ ± z* (s/√n)
Standard Error (SE) = s/√n
Margin of Error (ME) = z* × SE
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 11-12
Related Recommendation
90% Confidence Interval for Mean Additional Tax Owed - Estate Tax Returns
90% Confidence Interval for Mean Additional Tax Owed in Estate Tax Returns
90% Confidence Interval for Additional Estate Tax Owed
Constructing a 99% Confidence Interval for Population Mean Income
90% Confidence Interval for Average Daily Expenditures - Apex Solutions