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    Question

    A study estimates the average weight of a population

    with a 95% confidence interval of (65 kg, 75 kg). What does this mean?
    A The true population mean weight is exactly 70 kg. Correct Answer Incorrect Answer
    B 95% of the population has weights between 65 kg and 75 kg. Correct Answer Incorrect Answer
    C There is a 95% chance that the sample mean lies between 65 kg and 75 kg. Correct Answer Incorrect Answer
    D There is a 95% chance that the population mean lies between 65 kg and 75 kg. Correct Answer Incorrect Answer
    E The interval guarantees the population mean is within the range. Correct Answer Incorrect Answer

    Solution

    A confidence interval estimates the range within which the true population parameter (e.g., mean) is likely to fall, given the sample data. In this case, there’s a 95% probability that the interval (65 kg, 75 kg) includes the true mean weight of the population. Confidence intervals help quantify the uncertainty associated with estimates, providing more context than point estimates alone. Why Other Options Are Wrong : A) The mean might not be exactly 70 kg; it’s just an average of the range. B) Confidence intervals describe means, not individual values in the population. C) The interval relates to the population mean, not the sample mean. E) Confidence intervals provide a probabilistic estimate, not a guarantee.

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