An investigator wants to estimate the mean birth weight of infants born full term to mothers who are 19 years of age or younger. The mean birth weight of infants born full term to mothers 20 years of age and older is 3510g with a standard deviation of 385g.Part A. How many women 19 years of age or younger must be enrolled in the study to ensure that a 95% confidence interval estimate of the mean birth weight of their infants has a margin of error not exceeding 100g?Part B. How many do you need if 5% deliver pre-term?

Question
Asked Oct 29, 2019

An investigator wants to estimate the mean birth weight of infants born full term to mothers who are 19 years of age or younger. The mean birth weight of infants born full term to mothers 20 years of age and older is 3510g with a standard deviation of 385g.

Part A. How many women 19 years of age or younger must be enrolled in the study to ensure that a 95% confidence interval estimate of the mean birth weight of their infants has a margin of error not exceeding 100g?

Part B. How many do you need if 5% deliver pre-term?

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Expert Answer

Step 1

Part (A)

The provided information are:

Confidence level = 95% = 0.95

So, significance level (alpha) = 1-0.95 = 0.05

Margin of error (E) = 100

Population standard deviation (σ) = 385.

Step 2

The required value of z can be found using z-table.

0,05
1.96 (Using z-table)
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0,05 1.96 (Using z-table)

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Step 3

The required sample size can be...

x
1.96 x 385
100
=56.942
= 57
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x 1.96 x 385 100 =56.942 = 57

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