Asample of 14 joint specimens of a particular type gave a sample mean proportional limit stress of 8.48 mpa and a sample standard deviation of .79 mpa ("characterization of bearing strength factors in pegged timber connections, "j. of structural engr., 1997: 326-332). assume the population has normal distribution. calculate a 95% lower confidence bound for the true average proportional limit stress of all such joints. calculate a 95% confidence interval for the true average proportional limit stress of all such joints.

lower bound-8.106

8.02≤μ≤8.93 is the confidence interval

Step-by-step explanation:

given

mean(x)=8.48 MPa

standard deviation(s)=0.79 MPa

as we dont know the population standard deviation  so we use t-stat

formula

tα,n-1=t=}" alt="\frac{s}{√n}" />}" />

where

s-sample standard deviation

x-sample mean

μ-population mean

n-sample size

for 95% confidence interval and 13 degrees of freedom

t=1.771 (one tail ,as only lower bound is needed)

for lower bound

x-t×≤μ

8.48-1.771×≤μ

μ≥8.106

confidence interval

t=2.160 (two tailed)

x-t×≤μ≤x+t×

8.48-2.160×≤μ≤8.48+2.160×

8.02≤μ≤8.93 is the confidence interval required

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step-by-step explanation:

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