Question
A large company wants to estimate the average salary of
its employees. Instead of surveying all employees, the HR department randomly selects 200 employees and calculates the sample mean salary. Which of the following statements is the best justification for using the sample mean to estimate the population mean salary? ÂSolution
Explanation : - The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that regardless of the original population distribution, the distribution of the sample mean will approximate a normal distribution if the sample size is sufficiently large (typically n≥30n ). This theorem is essential in inferential statistics because it allows us to make reliable inferences about a population using a sample.  In the given question, the company wants to estimate the average salary of its employees. Since surveying every employee is impractical, they take a random sample of 200 employees . The CLT ensures that the sample mean salary will be normally distributed , even if the original salary distribution is skewed or non-normal. Â
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