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      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?  
      A The sample mean always equals the population mean, regardless of the sample size. Correct Answer Incorrect Answer
      B The distribution of salaries in the sample will always be normal, even if the population distribution is highly skewed. Correct Answer Incorrect Answer
      C The sample mean is an unbiased estimator of the population mean, and by the Central Limit Theorem, the sampling distribution of the sample mean approaches normality for large sample sizes. Correct Answer Incorrect Answer
      D The variability of the sample mean is independent of the sample size. Correct Answer Incorrect Answer
      E The Central Limit Theorem applies only if the original population distribution is normal. Correct Answer Incorrect Answer

      Solution

      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.  

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