Answer:
We accept H₀
Step-by-step explanation:
Population mean μ₀ = 47500
Population standard deviation unknown
Sample size n = 86 degree of freedom df = 86 - 1 df = 85
Sample mean μ = 48061
Sample standard deviation 2,351
The claim implies a two tail test with t-studend distributon
Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ ≠ μ₀
Confidence Interval mean α = 0,02 and α/2 = 0,01
With α/2 and df = 85, from t-table we find t(c) critical value
t(c) = 2,3710
We compute t(s) as
t(s) = ( μ - μ₀ ) / s /√n
t(s) = ( 48061 - 47500 )/ 2351/√86
t(s) = 561 * 9,273 / 2351
t(s) = 2,212
Now we compare t(s) and t(c)
t(s) < t(c) 2,212 < 2,371
Then we are in the acceptance region. We accept H₀
