Answer:
We need to develop a one-tail t-student test ( test to the right )
We reject H₀ we find evidence that student spent more than 24,5 hours on the phone
Step-by-step explanation:
Sample size n = 15 n < 30
And we were asked if the mean is higher than, therefore is a one-tail t-student test ( test to the right )
Population mean μ₀ = 24,5
Sample mean μ = 25,7
Sample standard deviation s = 2
Hypothesis Test:
Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ > μ₀
t (c) = ?
We will define CI = 95 % then α = 5 % α = 0,05 α/2 = 0,025
n = 15 then degree of freedom df = 14
From t-student table we get: t(c) = 2,1448
And t(s)
t(s) = ( μ - μ₀ ) / s/√n
t(s) = (25,7 - 24,5) /2/√15
t(s) = 2,3237
Now we compare t(c) and t(s)
t(c) = 2,1448 t(s) = 2,3237
t(s) > t(c)
Then we are in the rejection region we reject H₀ we have evidence at 95% of CI that students spend more than 24,5 hours per week on the phone
