Answer: 29.7188
Step-by-step explanation:
As we consider the given description, we have
n= 40
s= 112.08
Since population standard deviation is unknown , so we use t-test.
Using t-value table , the critical t- value will be:-
[tex]t_{n-1,\ \alpha/2}=t_{39,\ 0.05}=1.677[/tex]
The formula to find the margin of error :
[tex]E=t_{n-1,\ \alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
[tex]E=(1.677)\dfrac{112.08}{\sqrt{40}}\\\\=(1.677)(17.7214040076)\\\\=29.7187945207\\\\\approx29.7188[/tex]
Hence, the margin of error =29.7188
