Newborn jaundice is when a baby has a high level of biliru- Nood. Bilirubin is a

Question

Newborn jaundice is when a baby has a high level of biliru- Nood. Bilirubin is a yellow substance produced by the normal d cells. We would like to estimate the mean serum We breakdown of red blood ilevel of 4-day old infants using a sample of 150 infants. The ob- bilirtu s mple mean for these 150 infants is 5.96 mg/100 cc. Since the is large, we construct a 95% confidence interval for the mean ple size sampie s and we obtain the interval [5.3279; 6.5921] we based on z, Compute the estimated standard error of the mean. al Give the value of the sample standard deviation for these 150 infants,. c) Without computing the interval, would you expect a 97% confidence interval for the mean to be larger, smaller or of the same length compared to the above 95% confidence interval. (Why?) (d) Give a 97% confidence interval for the mean serum bilirubin level of 4-day old infants.

Explanation / Answer

A) At 95% confidence interval the critical value is 1.96

5.3279 = 5.96 - 1.96 * SD/sqrt (150)

Or, 5.3279 - 5.96 = - 1.96 * SD/sqrt (150)

Or, -0.6321 = -1.96 * SD/sqrt (150)

Or, SD/sqrt(150) = 0.6321/1.96

Or, SD/sqrt(150) = 0.3225

SO the standard error is 0.3225

B) standard deviation = 0.3225 * sqrt(150) = 3.95

C) At 97% confidence interval the margin of error Will be greater than the margin of error at 95% confidence interval.

SO the interval at 97% confidence interval will be larger than the interval at 85% confidence interval.

D) At 97% confidence interval the critical value is 2.17

Confidence interval is

Mean +/- z* * SD/sqrt (n)

= 5.96 +/- 2.17 * 3.95/sqrt(150)

= 5.96 +/- 0.7

= 5.26, 6.66

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