Question

# Find the margin of error for the given values of​ c, s, and n. c=0.80​, s=3.4​,...

Find the margin of error for the given values of​ c, s, and n.

c=0.80​,

s=3.4​,

n=14

Population standard deviation is not given. 's' is given. So, the Confidence Interval uses t-distribution.

We assume that random sample is taken from approximately normal distribution.

Given:
s=sample standard deviation =3.4
n=sample size =14
c=confidence level=0.8
Thus,
alpha=1-c=1-0.8=0.2
df=degrees of freedom of t-distribution=n-1=14-1=13

For two tailed test, critical value can be obtained either by using Statistical table or Software as:
t(alpha/2,df)=t(0.1,13)=1.350171

E=Margin of Error= t(alpha/2,df)*s/sqrt(n) = 1.226885
E=1.226885

R-commands and outputs:
s=3.4
n=14
c=0.8
alpha=1-c
alpha
[1] 0.2
tc=qt(1-alpha/2,df=n-1)
tc
[1] 1.350171
E=tc*s/sqrt(n)
E
[1] 1.226885

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