A team of clinical researchers is investigating the efficacy of a new intensive lifestyle modification program on glycemic control in patients with newly diagnosed type 2 diabetes. In a study of patients, the mean reduction in hemoglobin A1c (HbA1c) after six months is . The sample standard deviation for this reduction is . Assuming a normal distribution of the data and using a critical z-score of for the confidence level, what is the upper bound of the confidence interval for the mean reduction in HbA1c in this population? (Express your answer to three decimal places.)
Answer: 1.298 %
Answer
1.298
The confidence interval provides a range of values within which the true population mean is expected to fall. It is calculated using the sample mean, the standard error of the mean, and the corresponding z-score. The standard error (SE) is determined by dividing the standard deviation by the square root of the sample size (). The margin of error is the product of the z-score and the SE (). The upper bound is calculated by adding this margin to the sample mean ().
Step-by-Step Solution
Key Concept
The confidence interval for a sample mean is calculated as , where Standard Error is the standard deviation divided by the square root of the sample size.