Is there enough evidence, at the α = 0.05 level of significance, to suggest the standard deviation is not 3.1 ounces?

Question

A manufacturer of soda fountain machines claims its machine dispense liquid with a standard deviation of 3.1 ounces. A random sample of 20 machines found the standard deviation to be 4.6 ounces. Is there enough evidence, at the α = 0.05 level of significance, to suggest the standard deviation is not 3.1 ounces?

Answer 1

Since the statement says not, this is a 2-sided test. Thus, as 4.6 > 3.1, we can find the chi-squared cutoff using a cumulative probability of .975 or a right tail of .025

As n = 20, we have 19 df

From Excel, chisq.inv.rt(.025,19) = 32.8523268617297

(n-1)s²/σ² = 19 * 4.6²/3.1² =

As 41.8355879292404 > 32.8523268617297, we reject the null hypothesis that the standard deviation is 3.1