140k views
4 votes
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.55 MPa and a sample standard deviation of 0.76 MPa. (a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.) MPa

User Peli
by
8.2k points

1 Answer

6 votes

Answer:

95% of the lower confidence interval for the true average proportional limit stress of all such joints

7.7829

95% of the confidence interval for the true average proportional limit stress of all such joints

(7.7829, 9.3171)

Explanation:

Step(i):-

Given that the sample size 'n' = 12

Mean of the sample = 8.55

The standard deviation of the sample (S) = 0.76

Step(ii):-

95% of the confidence interval is determined by


(x^(-) - t_{(\alpha )/(2) } (S)/(√(n) ) , x^(-) + t_{(\alpha )/(2) } (S)/(√(n) ))

Degrees of freedom = n-1 = 12-1 = 11

t₀.₀₂₅ = 3.4966


(8.55 - 3.4966(0.76)/(√(12) ) , 8.55 + 3.4966 (0.76)/(√(12) ))

(8.55 - 0.7671 , 8.55+0.7671)

(7.7829, 9.3171)

Final answer:-

95% of the confidence interval for the true average proportional limit stress of all such joints

(7.7829, 9.3171)

User Quinestor
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.