Assignment 3: Law of Large Numbers

The definition for the law of large numbers states that the greater amount of experiments taken will have a better representation of the population. The sample mean is closer to the theoretical mean with the more data that is collected. (2008)

References:

MacEwan, B. (2008, spring semester). Psychology 261. Class Lectures. University of Mary Washington.

(Done by Carolyn & Kate)

Assignment 3: Changing your Oil

You waited: 3,467 miles

Mean waiting time: 3,258

Standard Deviation: 223 miles

z-score = (3,467-3,258)/223 = .9372

P (.94) = .1736

The fact that P is .1736 tells us that over 17% of the population waits longer than I did to get my oil changed. Also, I am within one standard deviation of the mean, and therefore I really did not wait unusually long to get my oil changed.

References:

Z-distribution. Retrieved February 2, 2008, from http://math2.org/math/stat/distributions/z-dist.htm

(Done by Carolyn & Kate)

Assignment 3: Proportion of Male Psychology Majors

In the following article, http://www.encyclopedia.com/doc/1G1-132241867.html, the authors state that 75% of all psychology majors nationwide are female, and 25% are male.

Before we did research about the proportion of psychology majors nationwide, we thought that more males would be represented nationwide in the psychology major as compared to our class. We thought that our school might not be representative of the entire nation because of the male-female ratio at Mary Washington, with so many more females at this school. However, we found that the proportion of males in our lab class is very similar to the nationwide proportion.

In our class, 6/25 students are male, which is 24%. This is very representative of the proportion of male psychology majors nationwide. Especially at a school which is predominantly female, it would be expected to find such a large gap between females and males.

References:

Bailly, M.D., King, A.R., McCray, J.A. (2005). General versus gender-specific attributes of the Psychology major. Journal of General Psychology, Retrieved February 2, 2008, from http://www.encyclopedia.com/doc/1G1-132241867.html

MacEwan, B. (2008, spring semester). Psychology 261. Class Lectures. University of Mary Washington.

Law of large numbers. (2008) Encyclopedia Britannica. Retrieved February 2, 2008, from http://www.britannica.com/eb/article-9384410

Z-distribution. Retrieved February 2, 2008, from http://math2.org/math/stat/distributions/z-dist.htm

(Done by Carolyn & Kate)

Assignment 3: Example from our life that illustrates the principle of the law of large numbers

An example from our lives that would illustrate the principle of the law of large numbers is the time that we go to bed. Both of us usually go to bed around the same time each night. However, there are times when we are sick and go to bed early, and there are also times when we have big papers due, and stay up really late. If you were to collect data from one of us during a week where we were sick, or had a paper due, the data would not be very representative of when we usually go to sleep. However, if you were to collect data over a long period of time, you would see that these early nights, or very late nights are outliers. You would not be able to see this, however, if you just had a few data points. This illustrates the Law of Large Numbers, which says that the more data points that you collect, the closer your mean will be to the true mean.

A strength of using this method is that the more data that is taken, the more representative the mean will be of what truly occurs. For example our bedtime would be better represented if we recorded the times we went to bed for five months. This amount of data would be a better representation than if we were only to take data for one month. A weakness would be the outliers that are random, and affect the mean, but are not representative of the normal bedtime.

References:

MacEwan, B. (2008, Spring Semester). Psychology 261. Class Lectures. University of Mary Washington.

(Done by Carolyn & Kate)