The file ‘birthweight’ contains the weights (in grams) of a random sample of 100

Question

The file ‘birthweight’ contains the weights (in grams) of a random sample of 100 full-term babies born in the U.S. Use this dataset to calculate the following, the sample mean is 3451.2 and the sample standard deviation is 724.0019

the sample mean

the sample standard deviation

a point estimate for the mean weight of all full-term babies born in the U.S.

a 90% confidence interval for the mean weight of all full-term babies born in the U.S.

a 95% confidence interval for the mean weight of all full-term babies born in the U.S.

a 99% confidence interval for the mean weight of all full-term babies born in the U.S.

What happens to the width of the confidence interval as the confidence level increases from

90% to 95% to 99%? (Does it get wider or narrower?)

Explanation / Answer

sample mean=3451.2

sample standard deviation =724.0019

point estimate for the mean weight =3451.2

std error of mean =std deviation/(n)1/2 =724.0019/(100)1/2 =72.40019

for 90% CI and (n-1=99) degree of freedom ; t=1.6604

therefore 90% confidence interval for the mean weight=point estimate -/+ t*std error =3330.9874 ; 3571.4126

for 95% CI and (n-1=99) degree of freedom ; t=1.9842

therefore 95% confidence interval for the mean weight=point estimate -/+ t*std error =3307.5423 ; 3594.8577

for 99% CI and (n-1=99) degree of freedom ; t=2.6264

therefore 99% confidence interval for the mean weight=point estimate -/+ t*std error =3261.0477 ; 3641.3523

width of the confidence interval gets wider as the confidence level increases from 90% to 95% to 99%

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