To reduce the width of a confidence interval, we need to consider the factors that impact its calculation. The width of a confidence interval for the population mean is influenced primarily by the sample size and the confidence level:
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Sample Size (n): Increasing the sample size will reduce the standard error, which will lead to a narrower confidence interval. Therefore, option A (Increase the sample size) will result in a reduced interval width.
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Confidence Level: Increasing the confidence level (e.g., from 95% to 99%) will actually increase the width of the confidence interval, as a higher confidence level means you need to capture a wider range to ensure that the true mean is within that interval. So, option B (Increase the confidence level) will not reduce the interval width.
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Population Mean: Changing the population mean does not affect the width of the confidence interval because the confidence interval's width is determined by the variability of the data and sample size rather than the mean itself. Therefore, option C (Increase the population mean) does not reduce the interval width.
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Sample Mean: Similar to the population mean, changing the sample mean does not affect the width of the confidence interval. The sample mean affects the center of the interval, not its width. So, option D (Increase the sample mean) does not contribute to reducing the interval width.
Thus, the option that will result in a reduced interval width is:
A) Increase the sample size.
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