Salaries of 43 college graduates who took a statistics course in college have a mean, x, of $61,500. Assuming a standard deviation, 6, of $16,568, construct a 99% confidence interval for estimating the population mean u. Click here to view a t distribution table. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. $
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.
![**Problem: Constructing a Confidence Interval for College Graduate Salaries**
The salaries of 43 college graduates who took a statistics course in college have a sample mean \(\bar{x}\) of $61,500. With a standard deviation \(\sigma\) of $16,568, construct a 99% confidence interval for estimating the population mean \(\mu\).
**Resources Available:**
- [Link to a t distribution table]
- [Link to page 1 of the standard normal distribution table]
- [Link to page 2 of the standard normal distribution table]
**Confidence Interval Equation:**
To calculate the 99% confidence interval, use the formula for the confidence interval for a population mean:
\[ \mu = \bar{x} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \(\bar{x}\) = sample mean
- \(Z\) = Z-score corresponding to the desired confidence level
- \(\sigma\) = population standard deviation
- \(n\) = sample size
**Task:**
Complete the confidence interval calculation for \(\mu\):
\[ \boxed{\ }\ < \mu < \ \boxed{\ } \]
*Round to the nearest integer as needed.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd8a77b5-5a09-468e-84b3-a259ddc50800%2F8bc6095c-0faf-4eda-a78c-fc2087f06db3%2Fwmanqes_processed.jpeg&w=3840&q=75)
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