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Ms. Williams Problem

Online Random Number Generator

1= Girl

2=Boy

2 2 2 1 1 1 1 1 2 1 2 1 2 1 2 2 2 2 2 1 2 1 2 1 1 1 2 1 2 1 1 1 1 1 1 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 2 1 2 2 2 2 1 2 2 1 2 2 1 2 1 1 1 2 2 2 2 2 2 2 2 1 2 1 1 1 1 1 1 2 2 1

Ref: Daniels (2003)

Exactly three boys occured once in our data.

• 1/98= .0102

The probability of randomly selecting a mother who has three boys in a row is 1.02%.

There were 56% boys to 44% girls. If we extended the random number generator to 10,000, the proportion of boys would decrease and the percent of girls would increase because of the Law of Large Numbers. Small samples contain higher variability than bigger samples because larger samples even out randomness.  Therefore, larger samples are more reliable because the values vary less and cluster more around the mean.

Personal Example of the Law of Large Numbers

In a freshman student’s first semester at Mary Washington, they take five classes with five random teachers. Two of the five professors are poor teachers. The student assumes that all teachers at Mary Washington are bad teachers because 40% of the teachers their first semester were bad. If they stay at the University, they will see that the percentage is much lower than 40% (maybe closer to 10%) because the Law of Large Numbers will reduce the impact of randomness on the small sample of five teachers.

Male Psychology Majors

There are 8 out of 46 males in our class

• 8/46=.1739 or 17.39%

According to an article in the Journal of General Psychology, the percentage of male psychology students was 25% nationwide in 2005. Our proportion of males in our class is smaller than the national average because chance has such a pervasive impact on small sample sizes.  The uneven distribution of males to females at Mary Washington also biases our results.

Oil Change

You waited 3,467 miles to change your oil. The mean is 3, 258 miles with a SD of 223 miles.

z-score= (3,467-3,258)/223= .93721

Area below z-score .93721 = .17618

Area between median and z-score = .5-.1761= .3239= 32.39%

Above and below the mean= .5 + .3239= .8239= 82.39

Therefore, 82.39% of drivers wait 3, 467 miles before getting an oil change. You’re mild deviation does not seem unreasonable when phrased this way.

Strengths/Weaknesses

Strengths:

• There are multiple ways to answer the oil change problem and can display your knowledge of statistics in many ways.

Weakness:

• Human error

References:

Baily, M. (April 2005). General versus gender-specific attributes of the Psychology major. Journal of General Psychology. http://209.85.165.104/search?q=cache:K0kDBfts1X0J:www.encyclopedia.com/doc/1G1-132241867.html+statistic+male+psychology+major+undergraduate&hl=en&ct=clnk&cd=11&gl=us

Daniels, Michael (2003). Random Number Generator. Accessed January 31, 2008 at http://www.mdani.demon.co.uk/para/random.htm

MacEwen, B. (2008, spring). Psychology 261. Class lectures. University of Mary Washington

Done by Mike and Mara

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