Answer :
The standard error of the sample mean is 1.213
How to calculate the standard error of the sample mean?
Given,
c = 95% = 0.95
n = 42
lower limit = 13.4
upper limit = 18.3
Since standard deviation population is unknown, we use this formula to calculate standard error.
standard error = margin of error / [tex]t_{\alpha/2,d.f.}[/tex]
First, we calculate the t distribution value
[tex]t_{\alpha/2,d.f.}[/tex] = [tex]t_{(1-c)/2,n-1}[/tex]
= [tex]t_{(1-0.95)/2,42-1}[/tex]
= [tex]t_{0.025,41}[/tex]
To find the value use t table. So, [tex]t_{0.025,41}[/tex] = 2.0195
Next, we calculate the margin of error
margin of error = (upper limit - lower limit)/2
= (18.3 - 13.4)/2
= 4.9/2
= 2.45
Now, we can calculate the standard error. So,
standard error = 2.45 / 2.0195
= 1.213
Thus, the standard error of the sample mean is 1.213
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