Question

1. A study of fill volumes is conducted at a food canning factory to determine the level of consistency between the two filling lines, A and B. A random sample of 16 cans taken from line A has a sample average of 8.005 ounces and a sample standard deviation of 0.011 ounces. A similar sample of 11 cans is obtained from line B with a sample average of 7.997 ounces and a sample standard deviation of 0.007 ounces. The quality control manager is interested in finding evidence at the 0.05 level that the process standard deviations are different for line A and line B.
2. Which of the following pairs of hypotheses reflect the question of interest?

3. 		H0: µA= µB HA: µA≠ µB
   		H0: pA≤ pB HA: pA> pB
   		H0: σ A≤ σ B HA: σ A> σ B
   		H0: σA= σ B HA: σ A≠ σ B
   		H0: µA≥ µB HA: µA< µB

4. What's the value of the test statistic?

Which of the following is(are) the correct critical value(s)?

		-1.96, 1.96
		-2.947, 2.947
		-2.33, 2.33
		0.327, 3.52
		2.85

What is the correct decision?

		Don't Reject H0
		Reject H0
		Don't Reject HA
		Reject HA

Answer 1

Question 1: Which of the following pairs of hypotheses reflect the question of interest?

Answer :

The Correct option is H₀: σ_A= σ _B H_A: σ _A≠ σ _B
Because, as stated "The quality control manager is interested in finding evidence at the 0.05 level that the process standard deviations are different for line A and line B." which is best depicted by the chosen test hypothesis.

Question 2: What's the value of the test statistic?

Answer :

The test statistic for testing the hypothesis, is given as,

Question 3: Which of the following is(are) the correct critical value(s)?

Answer:

For a 2 tailed test

or are the test conditions, thus the critical values are

-2.947, 2.947

Question 4: What is the correct decision?

Answer :

Pertaining to the test condition in the previous question,

,

Thus the correct option is : Don't Reject H₀