Question

A sample 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.

Answer 1

Answer:

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=$\frac{x-μ}{[tex]\frac{s}{√n}$}[/tex]

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×$\frac{s}{√n}$≤μ

8.48-1.771×$\frac{0.79}{√14}$≤μ

μ≥8.106

confidence interval

t=2.160 (two tailed)

x-t×$\frac{s}{√n}$≤μ≤x+t×$\frac{s}{√n}$

8.48-2.160×$\frac{0.79}{√14}$≤μ≤8.48+2.160×$\frac{0.79}{√14}$

8.02≤μ≤8.93 is the confidence interval required