A standard machine produced 1 inch bolts with a variance of 0.0006. A random smaple of 25 bolts produced by a new machine yields a sample variance of 0.0005. The manufacturer is willing to buy the new machine if he can "prove" uning alpha = 0.05, that it produces 1 inch bolts with smaller variance
a) test the hypothesis Ho: sigma squared is greater than or equal to 0.0006 vs H1: sigma squared is less than 0.0006
b) construct 95% confidence intervals for sigma squared and sigma.
DOF=delta=n-1=24
alpha = 0.05
the estimator for sigma squared is S hat squared
(n-1)s hat squared/sigma squared is chi-squared 24
chi squared n-1, alpha=24,0.05 = (36.41503) is this the right table value?
Value of test statistic = chi squared = (n-1)S hat squared/sigma squared = (24)(0.005)/0.0006=200? so does this mean that s hat is sample varriance and sigma squared is variance? sorry about the confusing formulas I don't know how to put the symbols in for sigma s hat etc.
so in this case 200 is greater than the table value so do I reject or accept?
I think it's suppose to be 20 why did I get 200?
How do I begin to construct a 95% confidence interval for sigma and sigma squared?
a) test the hypothesis Ho: sigma squared is greater than or equal to 0.0006 vs H1: sigma squared is less than 0.0006
b) construct 95% confidence intervals for sigma squared and sigma.
DOF=delta=n-1=24
alpha = 0.05
the estimator for sigma squared is S hat squared
(n-1)s hat squared/sigma squared is chi-squared 24
chi squared n-1, alpha=24,0.05 = (36.41503) is this the right table value?
Value of test statistic = chi squared = (n-1)S hat squared/sigma squared = (24)(0.005)/0.0006=200? so does this mean that s hat is sample varriance and sigma squared is variance? sorry about the confusing formulas I don't know how to put the symbols in for sigma s hat etc.
so in this case 200 is greater than the table value so do I reject or accept?
I think it's suppose to be 20 why did I get 200?
How do I begin to construct a 95% confidence interval for sigma and sigma squared?