A pharmaceutical company is about to launch a new manufacturing process in addition to the existing one. The quality control manager believes that the new method results in a different variation in the weights of the capsules. To verify the claim, the samples from each production line were obtained and the results are below (in mg):

Production Line 1:

100.5	98.6	101.3	103.6	95.7
103.3	102.9	99.6	99.9	100.8
104.9	101.6	101.1	101.6	96.5

(Note: The average and the standard deviation of the data are respectively 100.8 mg and 2.52 mg.)

Production Line 2:

99.9	97.9	100.3	97.9	101.5
97.4	97.4	100.3	96.4	101
98.6	98.7

(Note: The average and the standard deviation of the data are respectively 98.9 mg and 1.62 mg.)

Use a 10% significance level to test the claim that the standard deviation of the capsule weights in the production line 1 is greater than the standard deviation of the capsule weights in the production line 2.

Procedure: Select an answer Two proportions Z Hypothesis Test Two means T (pooled) Hypothesis Test Two means T (non-pooled) Hypothesis Test Two variances F Hypothesis Test Two means Z Hypothesis Test Two paired means Z Hypothesis Test

Assumptions: (select everything that applies)

Step 1. Hypotheses Set-Up:

$\displaystyle {H}_{{0}}:$ Select an answer μ μ₁-μ₂ σ₁²/σ₂² p₁-p₂ =	, where Select an answer μ=μ₁-μ₂ is μ's are p's are σ's are the Select an answer difference between population means population proportions population standard deviations population means and the units are ? oz mg lbs kg
$\displaystyle {H}_{{a}}:$ Select an answer p₁-p₂ μ σ₁²/σ₂² μ₁-μ₂ ? > ≠ <	, and the test is Select an answer Left-Tail Two-Tail Right-Tail

Step 2. The significance level $\displaystyle \alpha=$ %

Step 3. Compute the value of the test statistic: Select an answer χ²₀ z₀ f₀ t₀ = (Round the answer to 3 decimal places)

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA	PVA
Provide the critical value(s) for the Rejection Region:	Compute the P-value of the test statistic:
left CV is and right CV is	P-value is

Step 5. Decision:

CVA	PVA
Is the test statistic in the rejection region?	Is the P-value less than the significance level?
? yes no	? no yes

Conclusion: Select an answer Reject the null hypothesis in favor of the alternative. Do not reject the null hypothesis in favor of the alternative.

Step 6. Interpretation:

At 10% significance level we Select an answer DO DO NOT have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.