Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
X : 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7,31.6
True standard deviation (σ) = 4
α = 0.01
Mean (m) of the data:
Σ(X) /n = 520.7/20
m = 26.035 = 26.04
Uaing calculator :
Sample standard deviation (s) = 4.785
Null hypothesis : μ = 25
Alternative hypothesis : μ > 25
Test statistic (t) : (m - μ) / (s/√n)
t = (26.04 - 25) / (4.785/√20)
t = 0.972
We can obtain the p value using the pvalue from t score calculator :
df = n - 1 = 20 - 1 = 19
Decision:
If p < 0.01 ; reject null
p(0.972, 19) = 0.1716
Since p > 0.1716 ; we fail to reject the Null
