Question

Prob-5

In a certain design, it is important that standard deviation of the current be less than 21 mA. In a test of n=18 parts, the sample standard deviation is found to be 18 mA. Can we be 90% confident that the standard deviation will not exceed 21 mA?

***Provide tep-by-step instructions how to solve without skipping steps***

Answer 1

Here, we need to test the hypothesis H₀:²=21mA against

H₁: ^2<21mA

Here, n=18

s²=324

The test statistic is given by ((n-1)s²)/²~Chi-sq(n-1)df

Substituting the values we get , the value of chi-square statistic is 12.4897<24.77

The table value corresponding to the chi square dist with 17 degrees of freedom is 24.77 and if the value of the test statitic less than 24.77 we reject the null hypothesis since it is a left tailed test at 10%level. Therefore, we may conclude with 90% confidence that the standard deviation will not exceed 21 mA.