## An automotive part must be machined to close tolerances to be acceptable to customers. Production specifications call for a maximum variance

Question

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?

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2 weeks 2021-11-22T01:00:21+00:00 1 Answer 0

## Answers ( )

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.