You want to obtain a sample to estimate a population mean age of the incoming fall term transfer students. Based on previous evidence, you believe the population standard deviation is approximately o = 5.6. You would like to be 99% confident that your estimate is within 2.4 of the true population mean. How large of a sample size is required?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Estimating Sample Size for Population Mean**
To estimate the population mean age of incoming fall term transfer students, follow these steps:
1. **Information Provided:**
- Population standard deviation (\(\sigma\)) is approximately 5.6.
- Desired confidence level is 99%.
- Margin of error is 2.4 years.
2. **Objective:**
- Determine the required sample size (\(n\)) to achieve the desired margin of error with 99% confidence.
3. **Instructions:**
- Do not round between calculation steps.
- Use technology to find the z-score corresponding to the 99% confidence level.
- Provide your answer as a whole number, representing the total number of people required in the sample.
- Use the correct rounding rule for determining sample size.
### Calculation Method
To find the required sample size (\(n\)), use the formula:
\[
n = \left( \frac{{z \times \sigma}}{E} \right)^2
\]
Where:
- \(z\) is the z-score for a 99% confidence level.
- \(\sigma\) is the population standard deviation (5.6).
- \(E\) is the margin of error (2.4).
By entering the values into this formula, you can calculate the needed sample size for a 99% confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F961e5e88-22ea-4869-b279-3bff5edd9f45%2Fccffdc8b-445b-4ac7-8332-f2dad36048f7%2F7539i77_processed.jpeg&w=3840&q=75)
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