The standard error of the sample mean is 1.237.
How to calculate the standard error of the sample mean?
Given,
c = 95% = 0.95
n = 42
lower limit = 13.0
upper limit = 18.0
Since standard deviation population is unknown, we use this formula to calculate standard error.
standard error = margin of error / tα/2,d.f
First, we calculate the t distribution value
tα/2,d.f = t₍₁₋₀.₉₅₎/₂,₄₂₋₁
= t₀.₀₂₅,₄₁
To find the value use t table. So, t₀.₀₂₅,₄₁ = 2.0195
Next, we calculate the margin of error
margin of error = (upper limit - lower limit)/2
= (18.0 - 13.0)/2
= 5/2
= 2.5
Now, we can calculate the standard error. So,
standard error = 2.5 / 2.0195
= 1.237
Thus, the standard error of the sample mean is 1.237
Learn more about standard error here:
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