Question
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.
Step by Step Solution
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