Respuesta :
Answer:
The p-value you would use to test the claim
p -value = 0.007
Step-by-step explanation:
Step(i):-
Given random sample size 'n' = 45
Mean of the Population = 18.0 c.m
Standard deviation of the Population(S.D) = 0.25 c.m
Mean of the sample = 17.9 c.m
Null hypothesis :-
H₀ : μ = 18.0 c.m
Alternative Hypothesis:
H₁ : μ ≠ 18.0 c.m
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{17.9-18 }{\frac{0.25}{\sqrt{45} } } = -2.688[/tex]
|Z| = |-2.688|
|Z| = 2.688≅ 2.7
Step(ii):-
P -value :-
The z-test statistic value = 2.7
P( Z>2.7) = 1- P(Z< 2.7)
= 1- ( 0.5+ A(2.7))
= 0.5 - A(2.7)
= 0.5 - 0.4965
= 0.0035
P( Z>2.688)= 0.0035
Given data is two tailed test
2 X P( Z>2.688) = 2 X 0.035 = 0.007
P-value = 0.007
we will choose level of significance ∝=0.05
P -value < 0.05
H₀ is rejected
Alternative Hypothesis is accepted
Final answer:-
The population mean of pencils produced in that factory have a mean length is not equal to 18.0 cm.
