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?

Answer:Since 36.25 is less than 42.56, we do not reject H_o.Step-by-step explanation:Given n=30, s^2=0.0005The test hypothesis isH_o:σ^2=0.0004Ha:σ^2 not equal to 0.0004The test statistic isχ^2= (n-1)×s^2/σ^2 = (30-1)*0.0005/0.0004=36.25Given 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.