Question

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

c=0.80,

s=3.4,

n=14

Answer #1

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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LOADING...
Click the icon to view the t-distribution table.
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