Question

please show all work:

A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is 0.12 ounce. The machine is overhauled with new components, and ten cans are filled to determine whether the standard deviation has changed. Assume the fill amounts to be a random sample from a normal population. 12.14, 12.05, 12.27, 11.89, 12.06, 12.14, 12.05, 12.38, 11.92, 12.14

Perform a hypothesis test to determine whether the standard deviation differs from 0.12 ounce. Use the α = 0.05 level of significance. Evaluate these machines using a Traditional Hypothesis Test.

Hypothesis with claim:

Draw the curve, labeling the CV, TV, and shading the critical region.

CV(s):

TV:

Decision:

Answer 1

Solution:

Given:

Population Standard Deviation=

We have to perform a hypothesis test to determine whether the standard deviation differs from 0.12 ounce.

level of significance =α = 0.05

Hypothesis with claim:

Claim: the standard deviation differs from 0.12 ounce.

Critical value:

df = n -1 = 10 - 1 = 9

Look in Chi-square critical value table for df = 9 and right tail area = 0.05 / 2 = 0.025

and find critical value.

and for left tail critical value , look for area = 1 - 0.025 = 0.975 and

and find critical value.

Thus we get:

Chi-square critical values : 2.700 and 19.023

Test statistic value:

where

Thus we need to make following table:

x	x^2
12.14	147.3796
12.05	145.2025
12.27	150.5529
11.89	141.3721
12.06	145.4436
12.14	147.3796
12.05	145.2025
12.38	153.2644
11.92	142.0864
12.14	147.3796

Thus

Thus

Draw the curve, labeling the CV, TV, and shading the critical region.

Decision: Since Test statistic value = 13.544 is not in the rejection region, we failed to reject null hypothesis H0.

Thus we conclude that there is not sufficient evidence to support the claim that: the standard deviation differs from 0.12 ounce.