An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications call for a maximum variance in the lengths of the parts of. 0004. Suppose the sample variance for 30 parts turns out to be s 2 =.0005. Use =.05 to test whether the population variance specification is being violated.

State the null and alternative hypotheses.

H0 : σ2

Ha : σ2

Calculate the value of the test statistic (to 2 decimals).

The p-value is What is your conclusion?

Question

Mathematics

Jenna Griffith

5 August, 02:02

An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications call for a maximum variance in the lengths of the parts of. 0004. Suppose the sample variance for 30 parts turns out to be s 2 =.0005. Use =.05 to test whether the population variance specification is being violated.

State the null and alternative hypotheses.

H0 : σ2

Ha : σ2

Calculate the value of the test statistic (to 2 decimals).

The p-value is What is your conclusion?

+4

Answers (1)

Know the Answer?

Erica Norman · Answer 1

Since 36.25 is less than 42.56, we do not reject H_o.

Step-by-step explanation:

Given n=30, s^2=0.0005

The test hypothesis is

H_o:σ^2=0.0004

Ha:σ^2 not equal to 0.0004

The test statistic is

χ^2 = (n-1) * s^2/σ^2 = (30-1) * 0.0005/0.0004=36.25

Given a=0.05, the critical value is χ-square with 0.95, d_f=n-1=29 = 42.56 (check χ-square table)

Since 36.25 is less than 42.56, we do not reject H_o.

So we can conclude that the population variance specification is being violated.