recommended adequate intake of calcium for adults in 1000 mg

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).

Solution

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