Below you can find the basic statistics for a sample of the birth weights of ful
ID: 3155625 • Letter: B
Question
Below you can find the basic statistics for a sample of the birth weights of full-term infants who ultimately died of AIDS.
Sample Mean (X-bar) = 2890 grams
Sample Standard Deviation (s) =683
Sample Size (n) = 21
Find the two-sided 95% confidence interval for the true mean of the birth weight for the population of full-term infants who ultimately died of AIDS.
What would be the 95% confidence interval if instead of just knowing the sample standard deviation (s=682.87) you would know the true value of the standard deviation of the population =682.87?
Explanation / Answer
a)
Note that
Margin of Error E = t(alpha/2) * s / sqrt(n)
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 2890
t(alpha/2) = critical t for the confidence interval = 2.085963447
s = sample standard deviation = 683
n = sample size = 21
df = n - 1 = 20
Thus,
Margin of Error E = 310.8978726
Lower bound = 2579.102127
Upper bound = 3200.897873
Thus, the confidence interval is
( 2579.102127 , 3200.897873 ) [ANSWER]
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b)
In that case, we can use the z distirbution.
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 2890
z(alpha/2) = critical z for the confidence interval = 1.959963985
s = sample standard deviation = 682.87
n = sample size = 21
Thus,
Margin of Error E = 292.0629566
Lower bound = 2597.937043
Upper bound = 3182.062957
Thus, the confidence interval is
( 2597.937043 , 3182.062957 ) [ANSWER]
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