Answer to Question #236971 in Statistics and Probability for blossomqt

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.