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Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years. Jack’s mean weight over the last nine weeks is 185 lbs. Over a period of a few months, Jack’s weight measurements are approximately normal, with a standard deviation of about 4 lbs. Assume that 4 lbs is the true standard deviation in Jack’s weight.

1. Derive the standard error of the mean (SE). Please enter values to three decimal places.

2. Compute the margin of error (m) for the 95% confidence interval for Jack's mean weight.

Answer :

Final answer:

The standard error of the mean (SE) for Jack's weight is 1.333 lbs. The margin of error (m) for the 95% confidence interval is 2.61 lbs.

Explanation:

To calculate the standard error of the mean (SE), we divide the standard deviation (σ) by the square root of the sample size (n). In this case, the standard deviation is 4 lbs and the sample size is 9, so the SE = 4 / √9 = 4 / 3 = 1.333 lbs.

The margin of error (m) for a 95% confidence interval is calculated by multiplying the critical value (z*) by the standard error (SE). The critical value for a 95% confidence interval is approximately 1.96. Therefore, the margin of error (m) = 1.96 * 1.333 = 2.61 lbs.

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