Assume that a sample is used to estimate a population mean µ. Find the 99% confidence interval for a sample of size 64 with a mean of 49.5 and a standard deviation of 20.3. Enter your answer as an open- interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). 99% C.I. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

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**Confidence Interval Calculation**

Assume that a sample is used to estimate a population mean \(\mu\). Find the 99% confidence interval for a sample of size 64 with a mean of 49.5 and a standard deviation of 20.3. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

\[ \text{99% C.I.} = \_\_\_\_\_\_ \]

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

**Note:** 
- \( \text{Size of sample (n)} = 64 \)
- \( \text{Sample mean} (\overline{x}) = 49.5 \)
- \( \text{Standard deviation} (s) = 20.3 \)

**Instructions for students**:
- Determine the critical value using the z-distribution for a 99% confidence level.
- Calculate the margin of error and use it to find the confidence interval.
- Provide the answer as an open-interval (accurate to one decimal place).
Transcribed Image Text:**Confidence Interval Calculation** Assume that a sample is used to estimate a population mean \(\mu\). Find the 99% confidence interval for a sample of size 64 with a mean of 49.5 and a standard deviation of 20.3. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). \[ \text{99% C.I.} = \_\_\_\_\_\_ \] Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. **Note:** - \( \text{Size of sample (n)} = 64 \) - \( \text{Sample mean} (\overline{x}) = 49.5 \) - \( \text{Standard deviation} (s) = 20.3 \) **Instructions for students**: - Determine the critical value using the z-distribution for a 99% confidence level. - Calculate the margin of error and use it to find the confidence interval. - Provide the answer as an open-interval (accurate to one decimal place).
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