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Working Backwards from the Confidence interval to Find the Sample Mean Sometimes when we read statistical studies, only the confidence interval is stated; however, if the confidence interval is known, we can work backwards to find the sample mean. Suppose a sample mean was used to construct an interval of $(40,48)$. What was the value of the sample mean?
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Answer
Final Answer: The value of the sample mean is \(\boxed{44}\).
Step 1 ：The confidence interval is calculated as the sample mean plus or minus the margin of error. Therefore, the sample mean would be the midpoint of the confidence interval.
Step 2 ：Given the confidence interval is \((40, 48)\).
Step 3 ：Calculate the sample mean as the average of the lower and upper bounds of the confidence interval, which is \((40+48)/2 = 44\).
Step 4 ：Final Answer: The value of the sample mean is \(\boxed{44}\).
