The first question was about obtaining probabilities, and showing the randomness of situations in which there is a 50/50 likelihood of a certain outcome. Mrs. Williams believed she was “wired” for having only boys, when really she just experienced a random occurrence.

The second question showed how the Law of Large Numbers can effect judgment when interpreting data. Our example of recording the times at which we arrive to class shows that with a small sample size of just a week, one would not obtain the most accurate read of our data. With a larger sample size, however, the experimenter would find a more representative statistic.

The third question relates to the class lecture by also displaying the significance of the Law of Large Numbers. While the ratio of males to females in our lab section was not that far off from the statistics on nationwide male psychology majors, the study still shows that one can find a more accurate statistic from a larger sample of data.

The last question relates to the weekly topic of reading the normal curve. By calculating the mileage at which the majority of people change their oil, we can determine whether or not we are waiting too long to change ours. Knowing how to read and interpret data from a normal curve was very helpful in proving a point to the “father” in this scenario.

Flaws and Weaknesses

There was the possibility of mathematical errors during the coin tossing process, because we both flipped a coin 50 times each with semi-different strategies. There is also the slight possibility that we made some statistical miscalculations when calculating the percentages of male psychology majors and the number of males in our class.

Sources

National Center for Education Statistics. (2006). Digest of Education Statistics. Retrieved February 3, 2008, from http://nces.ed.gov/programs/digest/d06/tables/dt06_258.asp

Team Sand. (2008). Sources. Retrieved February 3, 2008, from http://psyc261sand.wordpress.com/

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

We flipped a coin 100 times to calculate the likelihood of having exactly 3 boys in a row. Girls were represented by a “heads” toss, and boys were represented by a “tails” toss. After flipping the coin 100 times, we had 47 girl tosses, and 53 boy tosses. There were two times in the 100 throws where we had exactly 3 boy tosses in a row, so the probability we obtained was .02. If we were to flip the coin 10,000 times, the proportions we would find would likely be similar to the statistics we obtained. The proportions of males to females we calculated, 47% to 53%, is pretty close to 50/50. With more tosses, the proportions may even out a bit more, but our findings were close to half and half.

Personal Example of the Law of Large Numbers

Our example of how the Law of Large Numbers applies to us is when we arrive to class on time. Usually, we are both punctual and timely. However, there may be certain times when we get out of a preceding class late, or simply oversleep. If one was to collect data on when we arrive to class during a week when we were sick and oversleeping, they would not have an accurate representation of our usual behavior. If they were to collect data over the course of the semester, they would have a more accurate read of our punctuality. According to the formula for standard deviation, smaller samples yield larger variations because outliers would have a greater influence in effecting the mean of a smaller sample.

Proportion of Males in Our Class

Our lab section has 25 people, 6 males and 19 females (24% male, 76% female). We found that according to the National Center for Education Statistics, 22% of undergraduate psychology majors were male and 78% were female. While there is only a slight difference in percentages, the nationwide sample has a smaller percentage of males. This could be because of a larger sample number, or also because women currently outnumber men in population. This relates to class lecture because according the the Law of Large Numbers, one will obtain a more accurate read of proportional data with a larger sample size.

Why We Did Not Wait Too Long to Change Our Oil

Statistically speaking, the average mileage people wait to change their oil is 3,258 miles with a standard deviation of 223 miles. This means that 25% of people wait for up to 3,481 miles and 25% change their oil as early as 3,035 miles. If we change our oil at 3,467 miles, our calculated z-score would be .937 (X-mean/standard deviation). This shows that we did not wait too long, because we are still within the average 25% of people who wait longer than 3,258 miles, and the z-score is still less than 1.

This assignment puts into practice the ways to calculate the mean, median, mode, standard deviation, and variance that we have been talking about in class.  It also taught us how to use the SPSS system as well as the hand/calculator method in calculating these values.

Point 4: Sources and References

Shoemaker, Allen L. What’s Normal? Temperature, Gender, and Heart Rate. Journal of Statistics Education. 4, 2 (1996)

Notes from Lecture.

SPSS

Data from Assignment 1

Point 5: Flaws, Weaknesses and Limitations

There are slight variations between our hand calculations and the SPSS data, but nothing significant. Due to the small sample size, the mean may not have been completely representative as our average body temperature.

- The mean is the most influenced by extreme temperature values because it changes your representative average body temperature.  Even one extremely high or extremely low value can affect the calculations of your mean body temperature.  Mode is not affected at all because it is the number most frequently repeated within the data. Median is not usually affected because median shows the middle of the data, and outliers are usually in the beginning or the end of the line of data being extremely high or extremely low.

2. Why might these extremes have occurred?

- These extremes may have occurred because of systematic bias.  It is possible that one day, you took your temperature after coming in from the cold, eating or drinking something hot or cold, or being sick for a day.

3. Are extreme values rare and unusual or not?

- No, they are not rare and unusual because various factors throughout the day can affect our temperatures.   In the case of our outliers, they did not deviate that far from the rest of the data.  A very unusual temperature (for example, one girl said that she had a value of 91 degrees) could result from an error in the instrument used to gather data, in this case the thermometer.

4. How reliable do you think these extreme data values might be, can we count on them- why or why not?

-  We should not count on the extreme data because certain circumstances could have affected that one temperature read and would not necessarily be a representative measure of our usual body temperature.

5.  Why 98.6 is incorrect and where the data came from:

- The correct mean body temperature according to the article is 98.25 degrees Fahrenheit.  98.6 degrees Fahrenheit is incorrect because the data that supported this mean was taken over 100 years ago. Climate changes and unreliable thermometers could have led to this measurement.  Also, Wunderlich’s original methodology was cited to have had problems.

-Amy:  The difference between my arithmetic average temperature and the correct average temperature is 0.04.  The Standard Deviation within the article was 0.73 and my body temperature is closer to the mean.  My average body temperature is not particularly unusual because it is extremely close to the mean body temperature for people around the world.

-Julia: The difference between my arithmetic average temperature and the correct average temperature is 1.35.  The Standard Deviation within the article was 0.73 and my body temperature was further away. The average body temperature that I recorded is unusually cold because in general, I took my temperature immediately after being outside. This was not necessarily planned, but it ended up working out that way.

Amy’s body temperature is more representative of the idea that men are cooler than women, where Julia’s was not.  If we took more data throughout the semester, our mean might be affected because we could have a more representative sample of temperatures.  A larger sample could lead to a more accurate measurement because with a larger sample, various factors that come into play during the week that could cause an extreme outlier might not affect the data as much.

Amy’s body temperature in degrees Celsius is 36.78. Julia’s is 36.05.  The formula we used was C=(F-32) * 5/9. F= degrees in Fahrenheit.

Statistics: 

Median- 96.95

Mean- 96.9

Mode- 96.1

Standard Deviation- .955

Variance- .914

-Julia

Statistics
Temperature
Mean        98.2171
Median        98.1000
Mode        98.60
Std. Deviation        .62190
Variance        .387

Median- (35+1)/2=18 and the value for the 18th entry when put in order was 98.1

Mode- 98.6

Arithmetic Mean- 98.2

The Standard Deviation dividing by n was 0.609 and dividing by (n-1) was 0.618.

The Variance was 0.371

Amy

Our sources and references are the two digital thermometers that we used, and the notes and powerpoints from class.