Answer:
H0: μ = 100 ; H1: μ > 100 ;
Test statistic = 0.75 ;
We fail to reject null ;
Kindly check explanation for the rest
Step-by-step explanation:
Given that :
H0: μ = 100
H1: μ > 100
Sample mean, x = 100.6 ; n = 9 ; sample Standard deviation, s = 2.4
Test statistic :
(x - μ) ÷ s/sqrt(n)
(100.6 - 100) ÷ 2.4 / sqrt(9)
0.6 ÷ 0.8 = 0.75
Probability of not rejecting the null :
P = P(Z > 0.75) = 0.22663
α = 0.05
Since, P > α ; we fail to reject the Null ; there is no sufficient evidence to accept the claim that mean strength is > 100 psi
μ + Zcritical*s/sqrt(n)
Zcritical at (1 - α) = 1.645
100 + 1.645*(2.4/3)
100 + 1.316 = 101.316
(x - μ) ÷ s/sqrt(n)
(101.316 - 102) ÷ 2.4 / sqrt(9)
-0.684 ÷ 0.8 = 0.75
= - 0.855
P(Z < - 0.855) = 0.1963 (Z probability calculator).
95% lower confidence interval :
x - error margin, E
E = Zcritical * s/sqrt(n)
E = 1.645 * 0.8 = 1.316
100.6 - 1.316 = 99.284
From part c :
Interval becomes ;
(99.284, 101.316) ; this interval contains the hypothesized mean value of 100. Hence we fail to reject the null.
