Question

Residents are concerned about the speed of vehicles traveling on that road. Drivers seem to have a tendency to drive at high speeds on their way out of and into town, even though the speed limit is only 25 mph. Police officers often record the speeds of the vehicles and ticket those who are found to be speeding.  the speeds from a sample of 33 vehicles recorded throughout one weekday :

24
25
26
27
27
27
28
28
28
29
29
30
30
30
30
31
32
32
32
32
33
33
34
35
35
37
37
39
40
40
41
42
43

1. The police department would like to know if the average speed traveled by all drivers on Pattee Canyon Drive is greater than 5 mph above the speed limit (i.e. greater than 30 mph).  Define the parameter of interest, the null hypothesis, and the alternative hypothesis for this situation.
2. Check the appropriate assumptions by verifying the conditions necessary to conduct a t-test for a mean.  Include the graphical display you use to check the Normal 15-40 condition below (either use StatCrunch or create one by hand).  
3. Find the test statistic and P-value (and clearly label them) for your hypothesis test.  You must show your work for both calculations.  
4. The P-value is a probability.  Explain precisely what the P-value from #3 represents in the context of the problem (don’t yet make a conclusion).  
5. Make a conclusion based on your P-value and hypotheses in the context of the problem.
6. A resident of the area wants to construct a 95% confidence interval for the parameter you defined in #1 so they can present it to the Missoula City Council.  Report the interval and the formula you used to find it.  Even if you used your calculator to find the interval, you must report the formula with all of the appropriate values included.  Finally, interpret your interval in the context of the problem.
7. Clearly explain whether your confidence interval in #6 supports your conclusion in #5.
8. Radar speed signs are traffic calming devices that slow speeders down by alerting them of their speed.  Suppose that the City of Missoula would consider installing such a sign if they think that more than 40% of all drivers speed on Pattee Canyon Drive (i.e. that they travel faster than 30mph).  Consider a new parameter of interest p = proportion of all drivers traveling on Pattee Canyon Drive who travel faster than 30mph.  Conduct the appropriate hypothesis test for p as follows.  You’ll need to look back at the data file to find the sample proportion of vehicles who were found to be traveling faster than 30mph. State the appropriate hypotheses in terms of this parameter.Clearly verify the necessary assumptions. Calculate the test statistic and calculate the P-value. Make a conclusion in the context of the problem.

Answer 1

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