Ashville City Maintenance Chief wants to cut back on the costs of maintaining the city automobile fleet Knowing that the city cars are kept for only year, he feels that the citys periodic maintenance schedule may cost more than it is worth He randomly selects a sample of 300 cars Among those 300 cars, 75 cars receive no maintenance unless they break down The rest of the cars are maintained using the usual schedule At the end of the year he finds the results pertaining to average costs per vehicle in these two groups (shown below) What can you tell the Ashville City Maintenance Chief about this experiment is the difference across groups statistically significant at 95 confidence level Use the five step model to answer this question Write a sentence or two (using words, not just numbers ) summarizing your results for a wider audience Variable Costs per Vehicle No MaintenanceMaintained Cars X $625X $575 S 1 150 S 2 200 N 1 75 N 2 225 SAMPLE RESPONSE Step 1 Making Assumptions 1 Samples 1 and 2 are random and independent 2 Our variable is a long ordinal scale (rating) 3 The sampling Z distribution is normal (our sample is large enough (N 120 for both samples together )) Step 2 Stating the Hypotheses Research Hypothesis There is a difference between AA and Reg employees in terms of efficiency Null Hypothesis There is no difference between AA and Reg employees in terms of efficiency Step 3 Drawing the Sampling Distribution and establishing a critical region 0 83 Step 4 Computing the test statistic Sigma Z(obtained) Step 5 Placing Z obtained on the distribution and stating the conclusion Conclusion Z obtained is not in the critical region We fail to reject the null hypothesis with 95 confidence It appears that there is no difference between AA and Reg employees in terms of efficiency

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Oct 14, 2024

Ashville City Maintenance Chief wants to cut back on the costs of maintaining the city automobile fleet. Knowing that the city cars are kept for

Ashville City Maintenance Chief wants to cut back on the costs of maintaining the city automobile fleet. Knowing that the city cars are kept for only year, he feels that the citys periodic maintenance schedule may cost more than it is worth. He randomly selects a sample of 300 cars. Among those 300 cars, 75 cars receive no maintenance unless they break down. The rest of the cars are maintained using the usual schedule. At the end of the year he finds the results pertaining to average costs per vehicle in these two groups (shown below). What can you tell the Ashville City Maintenance Chief about this experiment: is the difference across groups statistically significant at 95% confidence level? Use the five step model to answer this question. Write a sentence or two (using words, not just numbers!) summarizing your results for a wider audience.

Variable Costs per Vehicle:

No MaintenanceMaintained Cars

X=$625X= $575

S₁ =150S₂ = 200

N₁ =75N₂ = 225

SAMPLE RESPONSE

Step 1.Making Assumptions

1.Samples 1 and 2 are random and independent.

2.Our variable is a long ordinal scale (rating)

3.The sampling Z distribution is normal (our sample is large enough (N>120 for both samples together))

Step 2.Stating the Hypotheses

Research Hypothesis:There is a difference between AA and Reg employees in terms of efficiency.

Null Hypothesis: There is no difference between AA and Reg employees in terms of efficiency.

Step 3.Drawing the Sampling Distribution and establishing a critical region.

-0.83

Step 4.Computing the test statistic

Sigma =

Z(obtained) =

Step 5. Placing Z obtained on the distribution and stating the conclusion.

Conclusion: Z obtained is not in the critical region. We fail to reject the null hypothesis with 95% confidence. It appears that there is no difference between AA and Reg employees in terms of efficiency.