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Find Shortest Commute Time

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I need to measure minutes to and from work versus the time of day I leave. The objective is to find the time of the day that takes the least amount of time to get to work from the data given.

I would like the results to include a bell curve if possible. What would be the best form of measure: linear regression or null hypothesis. Discuss confidence intervals usefulness based on the number of data points.

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Solution Summary

The solution presents an analysis of the data to answer the question "What departure time has the shortest average commute time?"

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Your goal is to find the time of the day that takes the least amount of time to get to work from the data given. In other words, you want find the average length of a one-way commute for each of your departure times (4 am, 9 am, 11 pm, etc.) and figure out which departure time gives you the shortest commute.

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First, let's see if times vary by day:

[see Excel workbook]

It seems as if Sunday has the shortest commutes. You leave on Sundays at 9 am (one week at 8 am) and return at 8 pm (one week at 7 pm). So, if it turns out that the shortest commute is either at 9 am or 8 pm, you might want to consider if the quick commute is a result of the time or the day of the week.

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Now, onto the real question. Let's look at the data sorted by time:

Time Average Average (no bad ...

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