The tensile strength of a fiber used in manufacturing cloth

The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 2 psi. A random sample of eight fiber specimens is selected, and the average tensile strength is found to be 127 psi. (a) Test the hypothesis that the mean tensile strength equals 125 psi versus the alternative that the mean exceeds 125 psi. Use (b) What is the P-value for this test? (c) Discuss why a one-sided alternative was chosen in part (a). (d) Construct a 95% lower confidence interval on the mean tensile strength.

Solution

(a) Test the hypothesis that the mean tensile strength equals 125 psi versus the alternative that the mean exceeds 25 psi. Use ? = 0.05.

The test hypothesis is
Ho:=125
Ha:>125

The test statistic is

t=(xbar-)/(s/vn)

=(127-125)/(2/sqrt(8))

= 2.83

Given a=0.05, the critical value is |t(0.05,df=n-1=7)|=1.9 (check student t table)

Since 2.83 is larger than 1.9, we reject Ho.

So we can conclude that the mean exceeds 25 psi