Question

If the standard deviation of hole diameter exceeds 0.01 millimeters, there is an unacceptably high probability that the rivet will not fit. Suppose that in a sample of 15, the standard deviation is 0.008 millimeter. Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeter? Use α = 0.10.

Answer 1

Given that $n=15$ and $\sigma=0.008$

$H_o=s =0.01$

$H_1=s >0.01$

By using chi-square test:

$\frac{\left(n-1\right)\left(s^2\right)}{\left(s^2\right)}$

$=\frac{14\left(0.008\times 0.008\right)}{0.0001}$

$=8.96$

The tabulated value of chi-square deg. of freedom at 14 is 6.57.

Here calculated chisquare> tabulated chi-square.

Therefore, we reject the null hypothesis.