Question

The breaking strength of hockey stick shafts made of two different graphite-kevlar composites yields the following results (in Newtons):

Composite 1:

482.8	469.6	441.6	460.6	478.2
456.1	480.4	496.5	493.7	473.2
467.6	453.3	453.2

(Note: The average and the standard deviation of the data are respectively 469.8 Newtons and 16.5 Newtons.)

Composite 2:

495.4	489.2	513	498.6	482
484	504.6	492	491.6	495
509.5	475.8	484.2	523.5	483.8
474.1	493	510.7

(Note: The average and the standard deviation of the data are respectively 494.4 Newtons and 13.48 Newtons.)

Use a 1% significance level to test the claim that the standard deviation of the breaking strength of hockey stick shafts made of graphite-kevlar composite 1 is greater than the standard deviation of the breaking strength of hockey stick shafts made of graphite-kevlar composite 2.

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

Assumptions: (select everything that applies)

• Sample sizes are both greater than 30
• Paired samples
• Population standard deviation are unknown
• Simple random samples
• Normal populations
• Population standard deviation are unknown but assumed equal
• The number of positive and negative responses are both greater than 10 for both samples
• Population standard deviations are known
• Independent samples

Step 1. Hypotheses Set-Up:

H0:H0: Select an answer μ₁-μ₂ σ₁²/σ₂² μ p₁-p₂  =	, where Select an answer μ's are μ=μ₁-μ₂ is σ's are p's are  the Select an answer difference between population means population means population standard deviations population proportions  and the units are Select an answer lbs Watt J N
Ha:Ha: Select an answer μ₁-μ₂ σ₁²/σ₂² p₁-p₂ μ  ? > ≠ <	, and the test is Select an answer Left-Tail Two-Tail Right-Tail

Step 2. The significance level α=α= %

Step 3. Compute the value of the test statistic: Select an answer f₀ χ²₀ t₀ z₀  = (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?
? no yes	? 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 1% significance level we Select an answer DO DO NOT  have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Answer 1