Question : Birth weights: A simple random sample of birthweights in the UnitedSt

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Question : Birth weights: A simple random sample of birthweights in the UnitedStates has a mean of 3433g. The standarddeviation of all birth weights is 495g. a) Using a sample size of 75, construct a 95% confidenceinterval estimate of the mean birth weigth in th eUnitedStates. b) Using a sample size of 75,000,construct a 95%confidence interval estimate of the mean birth weight in theUnitedStates. c) Which of the preceding confidence intervals iswider? Why?. Please i need help. Step-step working Question : Birth weights: A simple random sample of birthweights in the UnitedStates has a mean of 3433g. The standarddeviation of all birth weights is 495g. a) Using a sample size of 75, construct a 95% confidenceinterval estimate of the mean birth weigth in th eUnitedStates. b) Using a sample size of 75,000,construct a 95%confidence interval estimate of the mean birth weight in theUnitedStates. c) Which of the preceding confidence intervals iswider? Why?. Please i need help. Step-step working

Explanation / Answer

a) sample size, n= 75
standard error, e = / n = 495 / 75 = 57.16
for 95% confidence, z = 1.96
confidence interval = ± z e = 3433 ± (1.96 x57.16) = (3320.97, 3545.03)
b) sample size n = 75,000
standard error, e = / n = 495 / 75000 =1.81
for 95% confidence, z = 1.96
confidence interval = ± z e = 3433 ± (1.96 x1.81) = (3429.45, 3436.55)
c) confidence intervals in part (a) is widerbecause sample size is small.

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