Answer:
We accetp H₀
Step-by-step explanation:
Information:
Normal distribution
Population mean = μ₀ = 449
Population standard deviation σ unknown
Sample size n = 23 n < 30 we use t-student test
so n = 23 degree of fredom df = n - 1 df = 23- 1 df = 22
Sample mean μ = 448
Sample standard deviation s = 20
Significance level α = 0,05
1.-Hypothesis Test
Null hypothesis H₀ μ₀ = 449
Alternative hypothesis Hₐ μ₀ ≠ 449
Problem statement ask for determine decision rule for rejecting the null hypothesis. For rejecting the null hypothesis we have to get an statistic parameter wich implies that μ is bigger or smaller than μ₀
2.-Significance level α = 0,05 ; as we have a two tail test
α/2 = 0,025
Then from t - student table for df = 22 and 0,025 (two tail-test)
t(c) = ± 2.074
3.- Compute t(s)
t(s) = ( μ - μ₀ ) / s /√n
plugging in values
t(s) = (448 - 449) / 20 /√23 ⇒ t(s) = - 1*√23 /20
t(s) = - 0.2398
4.-Compare t(c) and t(s)
t(s) < t(c) - 0.2398 < - 2.074
Therefore t(s) in inside acceptance region. We accept H₀
