recommended adequate intake of calcium for adults in 1000 mg per day. To investi
ID: 3397014 • Letter: R
Question
recommended adequate intake of calcium for adults in 1000 mg per day. To investigate the calcium intake of people living below poverty level, researchers obtained a random sample of 18 adults below the poverty level and found a mean daily intake of calcium of 947.4 mg.Find and interpret 95% confidence interval for the population mean. assume that calcium intake is normal distributed and the population stars deviation is 188 mg.
a) determine the margin of error
b) Find 95% confidence interval fo rthe population mean
c) Interpret the confidence inteval. ( explain what it tells us about the estimated mean daily camlium intake for the population).
Explanation / Answer
a)
Margin of Error = Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
Mean(x)=947.4
Standard deviation( sd )=188
Sample Size(n)=18
Margin of Error = Z a/2 * 188/ Sqrt ( 18)
= 1.96 * (44.312)
= 86.852
b)
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=947.4
Standard deviation( sd )=188
Sample Size(n)=18
Confidence Interval = [ 947.4 ± Z a/2 ( 188/ Sqrt ( 18) ) ]
= [ 947.4 - 1.96 * (44.312) , 947.4 + 1.96 * (44.312) ]
= [ 860.548,1034.252 ]
c)
Interpretations:
1) We are 95% sure that the interval [ 860.548,1034.252 ]] contains the
true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contain the
population mean
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