Answer :
Answer:
The data in the question is incomplete, however I believe you are interested in knowing how to calculate margin of error ME and confidence interval CI given figures from a sampled experiment or research. The explanation box will guide you through.
Explanation:
Confidence interval CI is the range within which an outcome is expected to occur. Usually, it is tied to a percentage which suggest how sure you are that a particular outcome will occur.
Margin of error ME depicts the actual boundaries within which your prediction is permissible. Hence ME is denoted as ± thereby lying on both side of the bell curve.
The relationship between CI and ME is:
[tex]CI=M[/tex]± ME and ME=[tex]Z*\frac{D}{\sqrt{n} }[/tex]
M=sample mean
D=standard deviation
n=sample size
Z=confidence coefficient
Example:
At 98% confidence level, what is the margin of error and confidence interval estimate that from a sample size of 500 girls, the average weight is 40kg with a standard deviation of 20.
Solution:
From the question, we have the following data:
M=40kg
D=20
n=500
at 98% confidence level,
Z=2.33
because,
Z is the equivalent of p in a standard confidence coefficient table.
where p=1-[tex]\frac{\alpha }{2}[/tex]
but α[tex]=1-[/tex]confidence level=1-98%=0.02
∵p=1-[tex]\frac{0.02}{2}[/tex]=1-0.01=0.99
reading up .99 from the Z table we have
Z=2.33
now
ME=[tex]Z*\frac{D}{\sqrt{n} }[/tex]=[tex]=2.33*\frac{20}{\sqrt{500} }[/tex][tex]=2.33*0.89=2.08[/tex]
∵Margin of error=2.08
CI=M±ME=40±2.08
Lower bound=40-2.08=37.92
Upper bound=40+2.08=42.08
In summary, it means that the researcher is 98% confident that the average weight of the girls falls withing 37.92kg to 42.08kg