Number of Farms A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 92% confidence. Assume o=31. Use a graphing calculator and round the answers to one decimal place. Assume the population is normally distributed. 6 78 52 3 54 33 64 49 7 15 21 4 50 29 9 80 109 40 80 48 4 16 8 68 Send data to Excel <μ< X

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**Number of Farms**

A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 92% confidence. Assume \(\sigma = 31\). Use a graphing calculator and round the answers to one decimal place. Assume the population is normally distributed.

Data:
\[ 6, 78, 54, 33, 64, 4, 50, 29, 9, 80, 8, 52, 3, 49, 4, 109, 40, 80, 48, 16, 68, 7, 15, 21 \]

There is an option to send the data to Excel for further analysis and computation.

**Instructions for Calculation:**

1. Enter the data into a graphing calculator or statistical software.
2. Use the formula for the confidence interval for the mean of a normally distributed population:
   \[
   \bar{X} \pm Z_{\alpha/2} \left(\frac{\sigma}{\sqrt{n}}\right)
   \]
   where:
   - \(\bar{X}\) is the sample mean.
   - \(Z_{\alpha/2}\) is the critical value for the desired confidence level (found using standard normal distribution tables).
   - \(\sigma\) is the population standard deviation (31 in this case).
   - \(n\) is the sample size (24 in this case).

**Diagram Explanation:**

There are no graphs or diagrams included in the image to explain.
Transcribed Image Text:**Number of Farms** A random sample of the number of farms (in thousands) in various states follows. Estimate the mean number of farms per state with 92% confidence. Assume \(\sigma = 31\). Use a graphing calculator and round the answers to one decimal place. Assume the population is normally distributed. Data: \[ 6, 78, 54, 33, 64, 4, 50, 29, 9, 80, 8, 52, 3, 49, 4, 109, 40, 80, 48, 16, 68, 7, 15, 21 \] There is an option to send the data to Excel for further analysis and computation. **Instructions for Calculation:** 1. Enter the data into a graphing calculator or statistical software. 2. Use the formula for the confidence interval for the mean of a normally distributed population: \[ \bar{X} \pm Z_{\alpha/2} \left(\frac{\sigma}{\sqrt{n}}\right) \] where: - \(\bar{X}\) is the sample mean. - \(Z_{\alpha/2}\) is the critical value for the desired confidence level (found using standard normal distribution tables). - \(\sigma\) is the population standard deviation (31 in this case). - \(n\) is the sample size (24 in this case). **Diagram Explanation:** There are no graphs or diagrams included in the image to explain.
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