Answer to Question #203973 in Statistics and Probability for zainab

Question

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 mg100 cc. Assume that bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg100 cc.

Answer 1

$n=16 \\ \bar{x}= 5.98 \\ s=3.5 \\ H_0: \mu= 4 \\ H_1: \mu > 4$

Test statistic:

$t = \frac{\bar{x}- \mu}{s / \sqrt{n}} \\ = \frac{5.98-4}{3.5 / \sqrt{16} } \\ = 2.2629$

p-value = 0.01945

p-value<0.05

Reject H₀.

It is concluded that, population mean is greater than 4.

The 95 % confidence interval for the population mean:

$Z_{0.05/2}=1.96 \\ CI = \bar{x}±Z_{0.05/2} \times \frac{s}{\sqrt{n}} \\ = 5.98 ±1.96 \times \frac{3.5}{\sqrt{16}} \\ = 5.98 ± 1.715 \\ (4.265, 7.695)$