Final answer:
To calculate the error bound for a 98% confidence interval with a known population standard deviation and a sample mean of 68, we use the formula EBM = z * (σ/√n) with z being the z-score for the 98% level, which is 2.326. Substituting the standard deviation of 4 and a sample size of 16, the calculated EBM is 2.326.
Step-by-step explanation:
The question deals with finding an error bound (EBM) for a 98% confidence interval when the population standard deviation is known. The given sample mean is 68, and we need to find the EBM to construct the confidence interval for the population mean. To do this, we use the formula EBM= z * (σ/√n), where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
For a 98% confidence interval, we look at the provided z-scores and select z0.01 = 2.326 since, for a two-tailed test, 1% on each tail amounts to a total of 2% beyond the confidence bounds, which is the complement of the 98% confidence level. Now, we substitute the values into the formula. With σ = 4 and n = 16, we get EBM= 2.326 * (4/√16) = 2.326 * 1 = 2.326. Therefore, our error bound for the 98% confidence interval is 2.326.