Question

For problems 9 and 10, a machine shop claims that the measurements of the parts it produces are uniform with a standard deviation of 1.3 millimeters. A test sample of 31 parts from the shop has a standard deviation of 1.8 millimeters. 9. Give the null and alternative hypothesis and critical value(s). 10. Give the test statistic and use this to find if this result contradicts the shop's claim at a 10% level of significance.

Answer 1

9.

The null and alternative hypothesis is ,

H0 : 0 = 1.3; HQ:0 + 1.3

The test is two-tailed test.

Now , df=degrees of freedom=n-1=31-1=30

The critical values are ,

$\chi^2_{df,\alpha/2}=\chi^2_{30,0.10/2}=\chi^2_{30,0.05}=43.773$ ; The Excel function is , =CHIINV(0.05,30)

$\chi^2_{df,1-\alpha/2}=\chi^2_{30,1-0.10/2}=\chi^2_{30,0.95}=18.493$ ; The Excel function is , =CHIINV(0.95,30)

Reject to Qo not Reject Ho reject Ho 2 an x na

10.

The test statistic is ,

$\chi^2_{stat}=\frac{(n-1)s^2}{\sigma_0^2}=\frac{(31-1)1.8^2}{1.3^2}=57.5148$

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho.

Conclusion : Hence , the result is contradicts to the shopers claim at 10% significance level.