1. Suppose a researcher wish to estimate the average salary of a certain organization. Which has 900 employees.

a) What is the population? How many data values are in the population?

b) What is the parameter of interest?

c) Suppose a sample of 10 workers is selected and their salaries (in Rs.) are 3500, 4800, 5300, 3500, 4200, 5000, 4000, 3800, 4000, and 4200. Calculate a statistic that you would use to estimate the parameter.

d) Suppose that another sample of 10 workers is selected, would it be likely that the value of the statistic is the same as in part(c)? Why or why not? Would the value of the parameter remain the same?

Let's break down and answer each part of the problem.

### a) What is the population? How many data values are in the population?
- **Population:** The population refers to the entire group of individuals that the researcher is interested in studying. In this case, the population consists of all employees in the organization.
- **Number of data values in the population:** Since the organization has 900 employees, there are 900 data values in the population.

### b) What is the parameter of interest?
- **Parameter of interest:** The parameter of interest is the average (mean) salary of all employees in the organization. A parameter is a numerical value that describes a characteristic of the population.

### c) Suppose a sample of 10 workers is selected and their salaries (in Rs.) are 3500, 4800, 5300, 3500, 4200, 5000, 4000, 3800, 4000, and 4200. Calculate a statistic that you would use to estimate the parameter.
- **Sample Mean (Statistic):** The statistic that we would use to estimate the parameter is the sample mean. The sample mean can be calculated as follows:

\[
\text{Sample Mean} = \frac{\text{Sum of the sample salaries}}{\text{Number of workers in the sample}}
\]

Let's calculate it:

\[
\text{Sample Mean} = \frac{3500 + 4800 + 5300 + 3500 + 4200 + 5000 + 4000 + 3800 + 4000 + 4200}{10}
\]

\[
\text{Sample Mean} = \frac{42300}{10} = 4230 \text{ Rs.}
\]

So, the statistic (sample mean) is **4230 Rs.** This is an estimate of the population mean (parameter).

### d) Suppose that another sample of 10 workers is selected, would it be likely that the value of the statistic is the same as in part (c)? Why or why not? Would the value of the parameter remain the same?
- **Likelihood of the statistic being the same:** It is unlikely that the value of the statistic (sample mean) would be exactly the same if another sample of 10 workers is selected. This is because each sample is a random subset of the population, and the salaries in different samples are likely to vary, leading to different sample means.
  
- **Parameter remaining the same:** The value of the parameter (the true population mean) remains the same because the parameter is a fixed value that describes the entire population. It does not change regardless of the samples drawn from the population.

### Summary of Answers:
1. **Population:** All 900 employees in the organization.
2. **Parameter of interest:** The average (mean) salary of all employees in the organization.
3. **Statistic (Sample Mean):** 4230 Rs.
4. **Likelihood of same statistic:** Unlikely; the sample mean would probably be different in another sample. The population mean (parameter) would remain the same.

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Would you like to explore any of these concepts further or have any additional questions?

### Further questions you might consider:
1. What other statistics could be used to estimate the parameter?
2. How does the sample size affect the accuracy of the estimate?
3. What is the difference between a population and a sample?
4. How would you calculate the variance of the sample?
5. What assumptions are made when selecting a random sample?
6. How could the researcher reduce the variability of the sample mean?
7. What is the standard error, and how is it related to this problem?
8. What would happen if the researcher took a larger sample size, such as 50 workers?

**Tip:** When estimating population parameters, always remember that larger samples tend to provide more accurate estimates, reducing the variability in sample statistics.

Learn how to estimate the average salary of an organization using statistical sampling methods. This problem covers concepts like population, parameter of interest, sample mean calculation, and the variability in sample statistics. Suitable for students in Grades 10-12.

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