Extra Credit Project-Group 4–Statistics 245
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You are a P.I. (private investigator), hired by the Virginia Beach District Attorney’s
Office, to assist the prosecution in a murder case. The person accused of committing the crime in Virginia Beach, claims he was in route to Williamsburg at the time in question. The crime scene investigators put the time of death at precisely 10:00 pm. The suspect’s alibi hinges on a credit card receipt for gas at a Wawa store in Williamsburg at 10:35 pm. The suspect claims he left Virginia Beach at 9:40 pm, and is documented by a time recorded photo taken at a Virginia Beach bank ATM at 9:40 pm., prior to the murder taking place. Therefore, the basic assumption of his alibi is that he could not have committed the murder at 10:00 pm, then be in Williamsburg 35 minutes later (you want to try to disprove this).
Since you work for the prosecution, you want to disprove the defense’s claim that the drive would take more than 35 minutes (Ho: µ > 35) and show that the mean time from Virginia Beach to Williamsburg, at that time of the evening, could feasibly be in less than 35 minutes (Ha: µ < 35)
Therefore, if you can show that µ < 35, then his alibi is discredited, and he could
have committed the murder.
In order to have your evidence to hold up in court, not only must you show that the drive can be done in under 35 minutes, it must also stand up to scrutiny by the defense’s experts. Therefore, you must have multiple, random data.
Actual Data: These are the data values, in minutes, which you collected, by making the drive “n” times:
35.1 34.8 36.2 33.1 33.8 35.0 38.1 30.9 35.7
36.0 33.3 35.0 31.6 34.1 34.7 34.7 36.1 35.0
32.6 33.8 31.3 35.1 35.9 31.9 34.0 35.8 36.3
33.7 33.4 37.3 31.8 30.4 32.7 31.7 33.3 39.5
- Run a 1-Variable Stat analysis in your calculator and list the sample mean
and sample standard deviation.
- Construct a 99% confidence interval for the mean driving time.
- Perform a one-tail hypothesis test for the mean driving time, with a
significance level of .0001
- State both hypotheses
- Show the rejection region
- Compute the test statistic
- State the conclusion
(Remember, you may be called to testify regarding your findings, therefore, your
results need to be double-checked for accuracy. The defense will have their own
experts testify, in an attempt to refute your evidence!).
- Turn in ONE page with your group’s results…include all group member’s names on
the paper. Summarize your findings with respect to the court case…not “reject” or “fail to reject”. Keep in mind this is the KEY part of your report. Your audience is
attorneys, the judge, and jurists. Therefore, do not be “technical”. Connect
your findings and conclusions to the specifics of the case.
- Present your results to the rest of the court on Wed. Your group’s presentation
should take no longer than 10 min.
This report could add 10 points to your next test!