An economist wants to compare the average hourly rate charged by automobile mechanics in two suburbs. She randomly selects auto repair facilities from both suburbs and records their hourly rates (in dollars). The data are as follows:

Suburb 1:

40.4	41.8	40.1	41.1	44.5
40.8	32.2	49.2	47.6	35.8
40.8	38	40.7	48.9	37.8
44.1	48.8	30.9	40.7	42.4

(Note: The average and the standard deviation of the data are respectively 41.3 $ and 5.04 $.)

Suburb 2:

47.2	43.2	51.4	40.9	44.2
43.4	48.5	51	38.3	30
39.7	44.3	49.9	43.3	44

(Note: The average and the standard deviation of the data are respectively 44 $ and 5.52 $.)

Use 5% level of significance to decide whether there is a sufficient evidence that the average hourly rate charged by automobile mechanics in suburb 1 is less than the average hourly rate charged by automobile mechanics in suburb 2.

Hint: The standard deviation for the first sample appears to be different from the standard deviation of the second sample. To check this claim the two-tail F-test for two variances can be setup which will result in the p-value of 0.699. Use the significance level of 5% to interpret this as sufficient or insufficient evidence that the two populations have different standard deviations and then decide whether to use the pooled or non-pooled procedure.

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

Assumptions: (select everything that applies)

Step 1. Hypotheses Set-Up:

$\displaystyle {H}_{{0}}:$ Select an answer μ σ₁²/σ₂² p₁-p₂ μ₁-μ₂ =	, where Select an answer σ's are μ's are p's are μ is the Select an answer population means population proportions difference between population means population standard deviations and the units are Select an answer pesos CAN $ 100%
$\displaystyle {H}_{{a}}:$ Select an answer μ p₁-p₂ μ₁-μ₂ σ₁²/σ₂² ? < > ≠	, and the test is Select an answer Left-Tail Right-Tail Two-Tail

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

Step 3. Compute the value of the test statistic: Select an answer z₀ χ²₀ t₀ 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 yes	? yes no

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

Step 6. Interpretation:

At 5% significance level we Select an answer DO DO NOT have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.