Question

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

Composite 1:

479	505.3	471.1	488.6	467.2
483.4	491.1	481.2	480.7	484.5
470.9	480	472.6	485.4	469.1
482.2	478.2	490.7	468.1

(Note: The average and the standard deviation of the data are respectively 480.5 Newtons and 9.6 Newtons.)

Composite 2:

506	521	474.4	496.6	517.5
506.3	511.3	486.9	499.3	466.4
507.3	527

(Note: The average and the standard deviation of the data are respectively 501.7 Newtons and 18.26 Newtons.)

Use a 10% 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 less than the standard deviation of the breaking strength of hockey stick shafts made of graphite-kevlar composite 2.

Procedure: Select an answer

Two proportions Z Hypothesis Test

Two means T (non-pooled) Hypothesis Test

Two paired means Z Hypothesis Test

Two means Z Hypothesis Test

Two variances F Hypothesis Test

Two means T (pooled) Hypothesis Test

Assumptions: (select everything that applies)

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

Step 1. Hypotheses Set-Up:

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

Step 2. The significance level α=_____ %

Step 3. Compute the value of the test statistic: Select an answer (z₀ t₀ χ²₀ f₀) = ______(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 or yes	no or yes

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

Step 6. Interpretation:

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

Answer 1

1.procedure:2 variances F hypothesis test.

2.Assumptions: 1.normal population

2.population standard deviation are unknown but assumed equal.

3.simple random samples.

4.independent samples.

3.Ho: . Units are :N(newton since breaking strength is a kind of force)

4.H1:. Left-tailed test.

5.significance level:=10%=0.10

6.value of test statistic:

The provided sample variances are

s1²=333.42 and s2²=92.16 and the sample sizes are given by n1​=12 and n2​=19

The F-statistic is computed as follows:

7.rejection region:

Based on the information provided, the significance level is α=0.10, and the the rejection region for this left-tailed test is

R={F:F<FL​=1.912}.

8.p-value=0.993872

9.test-statistic=3.617>1.912 hence test statistic dienst lie in the reject kon region.

10.p-value=0.993872>0.10 no it is not less than the significance level.

11.do not reject the null hypothesis in favour of the alternative.

12At 10% significance level we do not have sufficient evidence to reject the null hypothesis in favour of the alternative hypothesis.

Please rate my answer and comment for doubts.