# Confidence interval: lower bound

A sample of 14 joint specimens of a particular type gave a same mean proportional limit stress of 8.48 MPa and sample standard deviation of 0.79 MPa.

a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. What, if any assumption did you make about the distribution of proportional limit stress?

b) Calculate and interpret a 95% lower prediction bound for the proportional limit stress of a single joint of this type.

Please see attached file for full problem description.

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#### Solution Preview

See the attached file.

Sample mean =8.48 MPa

Standard deviation s= 0.79 MPa

Significance level (alpha (a) ) corresponding to 95% confidence = 100%-95% =5% or 0.05

Degrees of freedom (df) for sample size , n= 14 is (n-1) or 14-1=13

t -critical (0.05, 13) = 1.771

The t critical value is obtained from t-distribution table with df = (n - ...

#### Solution Summary

The solution calculates the lower bound of confidence interval.