Strengths
Weaknesses
Z= (3,467 – 3,258)/223 The Normal Curve
Z-Score = .9372
Area below Z-Score = .17618 or 17.62%
Area above and below mean = .82382 or 82.38%
(.5+.32382=.82382)
Area between median and Z-Score = .32382 or 32.38%
(.5-.17618 = .32382)
This shows that 82.38% of all people wait 3,467 miles before having an oil change. Because this is such a high percent we believe that waiting this long to get an oil change is not too long.
MacEwen, B. (2008, spring). Psychology 261. Class lectures. University of Mary Washington.
Characteristics of the Normal Curve. Retrieved February, 4th, 2008 from http://math.youngzones.org/normal.html.
The Law of Large Numbers (LLN) is the theorem that describes how a random-variable stabilizes over a long period of time (MacEwen, 2008).
(Jakob Bernoulli first proved the law of large numbers in 1713. This stamp displays the formula and graph for the law of large numbers.)
For example, my roommate and I decide to roll a die to determine who cooks dinner each night. For every even number it’s my job to cook dinner and for every odd number it’s her job. For a week straight even numbers have been rolled. I started to get upset because my roommate never had to cook. But when I remember the law of large numbers I realize that it will all work out and my roommate will indeed have to do her fair share of cooking dinner… eventually. This is as long as we live together for a decent amount of time (at least 6 months). The random variation of even or odd numbers that have been rolled will eventually become a 50:50 ratio.
MacEwen, B. (2008, spring). Psychology 261. Class lectures. University of Mary Washington.
Law of large numbers. (2008). In Encyclopædia Britannica. Retrieved February 04, 2008, from Encyclopædia Britannica Online: http://www.britannica.com/bps/topic/330568/law-of-large-numb
A coin was tossed 100 times. Tails represented having a female and heads represented having a male. Exactly three males occurred in succession only twice.
This chart exhibits data that show the 51:49 male to female (heads to tails) ratio found from 100 coin tosses. Since exactly three males (heads) in a row occurred twice the probability of having exactly three males in succession is 2%. Therefore, the probability of Ms. Williams having three boys in succession is very rare.
100-(3-1)= 98
2/98= 0.02 or 2%
If we toss our coin 10,000 times, the random variable should stabilize to a 50:50 ratio, as the Law of Large Numbers states.
MacEwen, B. (2008, spring). Psychology 261. Class lectures. University of Mary Washington.
In our Introduction to Statistics class there are 8 males out of 46 students (MacEwen, 2008). This means that 17.39% of the students in our Introduction to Statistics class are male.
8/46 = .1739 or 17.39%
In 2005 the national average for undergraduate psychology majors was 25% male and 75% female (Bailly, 2005). This means that our psychology class falls under the average amount of male psychology majors. This could be due to the fact that our sample size of 46 students is too small to have chance not be taken into consideration. Also, the University of Mary Washington has a rather low ratio of male to female students. Both these are factors that contribute to our results.
MacEwen, B. (2008, spring). Psychology 261. Class lectures. University of Mary Washington.
Bailly, M., King, A., McCray, J. (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/1G1-132
Strengths:
Weaknesses:
The correct body temperature is not 98.6 degrees Fahrenheit, but 98.25 degrees Fahrenheit. This error is due to many factors such as; time it was recorded, random events, and precise instruments of measure. The original temperature was determined by Wunderlich.
Ariel’s:
98.25 degrees Fahrenheit – 97.8 degrees Fahrenheit = .45 F
Amanda’s:
98.25 degrees Fahrenheit – 97.3 degrees Fahrenheit = .95 F
Ariel’s standard deviation is lower than the average, which means she is a good representative. Amanda’s standard deviation is higher than the average, which means she is not as good of a representative, but it’s not far enough away from the average to be unusual.
Shoemaker, A. L.(1996). What’s Normal? Temperature, Gender, and Heart Rate. Journal of statistics Education. 4, 2.
Since both of our mean temperatures fell below the mean average for all women (98.25 F) and both our standard deviations are higher, we are not perfect representatives of the female race. However, our information does show that Ariel’s mean is a little less than one standard deviation from the actually mean of women, while Amanda’s is a little more than one standard deviation from the actually mean of women. Although our information doesn’t correlate perfectly, we do show having a colder temperature than your typical male. Since neither one of us is male, we can’t juxtapose our data, but over all we feel that we represent fairly well that women’s temperatures are lower on average.
This data might have been affected by systematic bias or random variation (i.e. where temperature is taken, if anything was eaten before, etc). Therefore, we do believe that by taking more data over a longer period of time we would have more accurate results. This is due to the fact that outliers would have more average data values to be compared to, making them affect our final mean less.
Shoemaker, A. L.(1996). What’s Normal? Temperature, Gender, and Heart Rate. Journal of statistics Education. 4, 2.
We believe that outliers are not reliable values because they do not represent a large part of the data. Therefore, we can not count on them to provide an accurate reading of our average daily body temperature.
MacEwen, B. (2008, Spring Semester). Psychology 261. Class Lectures. University of Mary Washington.
The mean in our data was most influenced by outliers. This is the case since an extremely high or low number altered our means more than mode or median. Mode was not affected because if we had an extreme temperature we only had it once. Since mode is the temperature that your body was the most, it was not affected. Also, median was not affected because we both had 34 temperatures after collecting our data. Since mode is the middle number when data is put in rank order, a high or low temperature did not affect it.
These extremes might have occurred based on random variation such as taking our temperature after eating ice cream. These occurrences we discovered to be rare and unusual due to the fact that we both took our temperatures at similar times a day, not before or after drastic workouts, food consumption, or activities outside.
MacEwen, B. (2008, Spring Semester). Psychology 261. Class Lectures. University of Mary Washington.
