Questions: In a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was 3436 with a standard deviation of 2598. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. 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. 90% of taxes owed for estate tax returns are between and . B. One can be 90% confident that the mean additional tax owed is between and . C. There is a 90% probability that the mean additional tax owed is between and

In a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was 3436 with a standard deviation of 2598. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. 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. 90% of taxes owed for estate tax returns are between and . B. One can be 90% confident that the mean additional tax owed is between and . C. There is a 90% probability that the mean additional tax owed is between and
Transcript text: In a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was $\$ 3436$ with a standard deviation of $\$ 2598$. Construct and interpret a $90 \%$ confidence interval for the mean additional amount of tax owed for estate tax returns. 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. $90 \%$ of taxes owed for estate tax returns are between $\$ \square$ and $\$ \square$. B. One can be $90 \%$ confident that the mean additional tax owed is between $\$$ and $\$$. C. There is a $90 \%$ probability that the mean additional tax owed is between $\$$ and $\$$
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Solution

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Solution Steps

Step 1: Calculate the Z-Score

For a \(90\%\) confidence level, the Z-Score (Z) is approximately \(1.6449\).

Step 2: Calculate the Margin of Error

The margin of error (ME) is calculated using the formula:

\[ \text{Margin of Error} = Z \times \frac{\sigma}{\sqrt{n}} \]

Substituting the values:

\[ \text{Margin of Error} = 1.6449 \times \frac{2598}{\sqrt{100}} = 427.333 \]

Step 3: Calculate the Confidence Interval

The confidence interval for the mean is given by:

\[ \bar{x} \pm Z \times \frac{s}{\sqrt{n}} \]

Substituting the values:

\[ 3436 \pm 1.6449 \times \frac{2598}{\sqrt{100}} = 3436 \pm 427.333 \]

Calculating the lower and upper bounds:

\[ \text{Lower Bound} = 3436 - 427.333 = 3008.67 \] \[ \text{Upper Bound} = 3436 + 427.333 = 3863.33 \]

Thus, the \(90\%\) confidence interval is:

\[ (3008.67, 3863.33) \]

Step 4: Interpretation of the Confidence Interval

One can be \(90\%\) confident that the mean additional tax owed is between \(\$3008.67\) and \(\$3863.33\).

Final Answer

The answer is B: One can be \(90\%\) confident that the mean additional tax owed is between \(\$3008.67\) and \(\$3863.33\).

\(\boxed{3008.67 \text{ to } 3863.33}\)

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