The population standard deviation of tensile strength is 2 psi. A random sample of 8 fiber specimens is selected & the average strength is found to be 127 psi.
a) Test the hypothesis that the mean tensile strength equals 125 psi vs the alternative that the mean exceeds 125 psi, use $α=0.05$.
b) Find a 95% lower confidence interval on the mean tensile strength. $$\\$$ This is what I've done so far:
a)
$H_o:μ = 125$
$H_a:μ > 125$
critical value = 1.645
Test Statistic:
$Z=\frac{\bar{x}-μ}{σ/\sqrt{n}}$ = $\frac{127-125}{2/\sqrt{8}}$ = 2.83
Since Z=2.83 > 1.645, we would reject $H_o$. $$\\$$
b) I'm not sure how to do part B.
I would appreciate your help, thanks!
Part B:
The formula for confidence interval for the certain problem is: $\bar{x}$ $\pm$ $Z(\frac{σ}{\sqrt{n}})$.
*Z= $Z_\frac{α}{2}$
= 127 $\pm$ 1.96$(\frac{2}{\sqrt{8}})$
= (125.61, 128.39)