Two independent simple random samples of professional NBA and NFL players heights are given below.



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Let by the population mean height for NBA players and be the population mean for NFL players. Find a 92% confidence interval . (Round answers to two decimal places.)

margin of error:
lower limit:
upper limit:



To find the 92% confidence interval for the difference in population means of NBA and NFL player heights, follow these steps:

1. **Calculate Sample Means and Standard Deviations**:
   - Calculate the sample means (\( \bar{x}_{NBA} \) and \( \bar{x}_{NFL} \)) and sample standard deviations (\( s_{NBA} \) and \( s_{NFL} \)) from the provided data.

2. **Determine the Sample Sizes**:
   - Let \( n_{NBA} \) be the sample size for NBA players and \( n_{NFL} \) for NFL players.

3. **Calculate the Standard Error (SE)**:
   \[
   SE = \sqrt{\frac{s_{NBA}^2}{n_{NBA}} + \frac{s_{NFL}^2}{n_{NFL}}}
   \]

4. **Find the Z-score for a 92% Confidence Level**:
   - The Z-score for a 92% confidence interval can be found in Z-tables or calculated as \( Z \approx 1.75 \) (since 92% leaves 4% in each tail).

5. **Calculate the Margin of Error (ME)**:
   \[
   ME = Z \times SE
   \]

6. **Construct the Confidence Interval**:
   - The confidence interval for the difference in means (\( \bar{x}_{NBA} - \bar{x}_{NFL} \)) is:
   \[
   (\bar{x}_{NBA} - \bar{x}_{NFL}) \pm ME
   \]

7. **Calculate the Lower and Upper Limits**:
   - Lower Limit: \( (\bar{x}_{NBA} - \bar{x}_{NFL}) - ME \)
   - Upper Limit: \( (\bar{x}_{NBA} - \bar{x}_{NFL}) + ME \)

Please upload the CSV file containing the sample data so that I can perform these calculations and provide you with the specific values.

Let by the population mean height for NBA players and be the population mean for NFL players. Find a 92% confidence interval. (Round answers to two decimal places.)

Explore how to calculate a 92% confidence interval for the difference in population means of NBA and NFL player heights. This guide includes step-by-step methods and key statistical concepts essential for understanding confidence intervals.

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