Question

A sample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.59 MPa and a sample standard deviation of 0.72 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 Interpret this bound. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value. What, if any, assumptions did you make about the distribution of proportional limit stress

Answer 1

(8.1744 ; 9.0056) ;

With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value.

Explanation:

Given that :

Sample size, n = 14

Mean, xbar = 8.59

Standard deviation, s = 0.72

Tcritical at 95%, df = 13 - 1 = 12 confidence level = 2.160

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/sqrt(n)

Margin of Error = 2.160 * 0.72/sqrt(14)

Margin of Error = 0.4156446

Lower confidence boundary :

8.59 - 0.4156 = 8.1744

Upper confidence boundary :

8.59 + 0.4156 = 9.0056

Confidence interval : (8.1744 ; 9.0056)

Hence, we can conclude with a confidence of 95% that the true mean proportional limit stress of all joints exists within the interval above.