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A 95% confidence interval is calculated for a sample of weights of 100 randomly selected pigs and the resulting confidence interval is 42 to 48 pounds. Will the sample mean weight fall within the confidence interval?

Question

A 95% confidence interval is calculated for a sample of weights of 100 randomly selected pigs and the resulting confidence interval is 42 to 48 pounds. Will the sample mean weight fall within the confidence interval?

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Solution

Yes, the sample mean weight will fall within the confidence interval. A 95% confidence interval means that 95 out of 100 times, the true population mean (average) will fall within the calculated range (in this case, 42 to 48 pounds). Since the sample mean is an unbiased estimate of the population mean, it will also fall within this interval.

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