Did I calculate this correctly. Thank you. ### Estimating Confidence Intervals for Mean Serum Indirect Bilirubin Levels in 4-Day-Old Infants#### Problem Statement:We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The mean for a sample of 16 infants was found to be 5.98 mg/100 cc. Assume that bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg/100 cc.#### Task:Using the data provided, calculate the 90%, 95%, and 99% confidence intervals for the mean of the bilirubin levels in 4-day-old infants. Hint: Treat it as a normal distribution.Given:- Sample Mean (\( \bar{X} \)) = 5.98- Standard Deviation (s) = 3.5- Sample Size (n) = 16#### Solution:1. **90% Confidence Interval:** - Degrees of Freedom (df) = n - 1 = 16 - 1 = 15 - \( t_{c} \) (critical t value) for 90% confidence with \( df = 15 \) is approximately 1.753. - Formula: \( \bar{X} \pm t_{c} \frac{s}{\sqrt{n}} \): \[ 5.98 \pm 1.753 \frac{3.5}{\sqrt{16}} \] - Calculation: \[ 5.98 \pm 1.753 \frac{3.5}{4} \implies 5.98 \pm 1.753 \times 0.875 \] \[ 5.98 \pm 1.535 \implies (4.446, 7.514) \] - **90% C.I:** (4.446, 7.514) 2. **95% Confidence Interval:** - \( t_{c} \) for 95% confidence with \( df = 15 \) is approximately 2.131. - Formula: \( \bar{X} \pm t_{c} \frac{s}{\sqrt{n}} \): \[ 5.98 \pm 2.131 \frac{3.5}{\sqrt

Name: Did I calculate this correctly. Thank you. ### Estimating Confidence
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Did I calculate this correctly. Thank you. ### Estimating Confidence Intervals for Mean Serum Indirect Bilirubin Levels in 4-Day-Old Infants#### Problem Statement:We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The