Respuesta :
Answer:
The test statistic t = 1.126 < 1.703 of '27' degrees of freedom at 0.05 level of significance.
null hypothesis(H₀ ) is accepted
There is evidence that the average breaking strength is 7.000.
Step-by-step explanation:
Step 1:-
Given random sample size (n) =28 <30
small sample size n= 28
The sample mean (x⁻) = 7.142
sample standard deviation (S) =0.672
Step 2:-
Null hypothesis :- there is evidence that the average breaking strength is 7.000.
H₀ : μ =7
Alternative hypothesis:-there is evidence that the average breaking strength is 7.000.
H₁ : μ ≠7
The test statistic [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
Substitute all values and simplification ,
[tex]t = \frac{7.142 -7}{\frac{0.672}{\sqrt{28} } } = \frac{0.142 }{0.1269}[/tex]
t = 1.126
Calculated value is t = 1.126
The degrees of freedom γ = n-1 = 28-1 =27
The tabulated value t= 1.703 at degrees of freedom at 0.05 level of significance.
since calculated t < tabulated value 't' value of 27 degrees of freedom at 0.05 level of significance.
null hypothesis(H₀ ) is accepted
There is evidence that the average breaking strength is 7.000.
