References:

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

(Done by Carolyn & Kate)

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)

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)

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)

• We did a random number generation on a TI-86 calculator, using only the numbers 0 and 1, assuming that 1s were boys:

0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1

• EXACTLY three boys in succession occurs four times (in bold and underlined)
• The event “exactly three boys in succession” is likely to occur…
  • 4 / (100-2) = .04
• MORE than three boys in succession occurs six times (in italics and underlined)
• The event “more than three boys in succession” is likely to occur…
  • 6 / (100-2) = .06
• The proportion of boys vs. girls in the sample of 100:
  • 61/100 = .61 (boys)
  • 39/100 = .39 (girls)

• If the coin was flipped 10,000 times, rather than 100 times, the proportion of boys would be a lot closer to .50. This is because although each individual coin toss is random, it is just as likely for it to be a head as it is a tail.

References:

TI-86 Calculator

(Done by Carolyn & Kate)

An obvious weakness in this activity is human error. In entering data into the calculator or SPSS, one could easily make a mistake. However, the calculator and SPSS are also strengths, because having to calculate these statistics by hand would create even more error. Some factors of weakness go back to our first assignment of taking our body temperatures. Factors such as weather, not being able to take your temperature consistently, eating hot or cold food, and other reasons add to reasons why these readings may not be the most reliable. Another weakness is the lack of data points collected. If we took our temperature for additional weeks it would help make our findings more accurate.

References:

Mac Ewen, B. (2008, spring semester). Psychology 261. Class lectures. University of Mary Washington

Shoemaker, A.L.(1996). What’s normal? Temperature, gender, and heart rate. Journal of Statistic Education. 4, (2).

The mean is the most influenced by outlier temperature values because it is averaged in with all of the other temperatures. An extreme temperature, whether it be very high or very low will be accounted for when calculating the average of all the temperatures and will have an affect on that data. The median is the number in the middle of all the data, so outliers would not really influence the median as much. An extremely high or low temperature would just be added to the sequence of numbers, not having a great affect on determining what the middle number is. The mode is the number that occurs the most often, and as we know, an outlier is one that is an extreme, and does not occur very frequently.

Why might these extremes have occurred?

Extremes temperature readings may have occurred because of many reasons. Weather, exercise, showers, food or beverages consumed, stress, and sickness could lower or raise our body temperatures. It is also important to take into consideration the measuring tool being used. If it does not seem like there are already so many random events that play a role in extreme temperature findings, it is possible that a faulty thermometer could be the reason.

Are extreme values rare and unusual or not?

According to our values and most of the classes, an extreme measurement was rare. There were usually only one or two temperature readings in each group that were extreme, and were usually influenced by some factor that caused the reading to be so different. Even though extreme values may be rare and can be frustrating to account for, they help to remind us that experiments are not perfect. It is important to take into consideration all the factors that may have an affect on your findings.

How reliable do you think these extreme data values might be?

These extreme data values are not very reliable, and should sometimes even be disregarded. This is because there is often a systematic bias that occurs in order to cause the extreme data values.

Look up the article by Allen L. Shoemaker to find out the correct body temperature, why 98.6 F is incorrect, and where this value came from.

According to the article, when measuring body temperature orally, the normal temperature is 98.25 F. The common idea of 98.6 F came about one hundred years ago, by Wunderlich. According to Shoemaker, Wunderlich was inaccurate due to faulty thermometers and diurnal fluctuations. The standard deviation of temperatures according to Shoemaker is 0.73.

How does the difference of your arithmetic average temperature and the Standard Deviation compare the the SD of body temperatures given in the article? Is your body temperature average particularly unusual? Explain.

Carolyn:

97.817 + .73 = 98.547

Although 97.817 F is below the normal body temperature of 98.25 F, it is within one standard deviation of the normal temperature, and therefore my body temperature is not particularly unusual.

Kate:

98.0667 + .73 = 98.7967

My body temperature is within one standard deviation of the normal body temperature of 98.25 as well.

How representative do you think your body temperature data are?

Carolyn:

I think that my body temperature data is quite representative of the normal body temperature. Although it is slightly cooler than the normal body temperature, it is still within one standard deviation of the normal body temperature. Although research shows that men are usually cooler, I feel as though I am usually cold, and so therefore it makes sense that my temperature would be cooler rather than warmer.

Kate:

According to the math my body temperature data is fairly close to the normal body temperature. Before this project the only time I ever took my temperature was when I was not feeling well. It was interesting to find that my average body temperature is pretty close to the norm. This is something that I never would have known if I was not given this assignment.

What might affect the mean of the data?

The mean of the data is affected by outliers in the data. Although neither of us had extreme outliers, the coolest and warmest temperatures would have affected the mean, especially considering that there were not that many data points recorded in the first place.

Do you think if you took more data, you’d be more or less accurate? Why?

With the addition of more data, we think that we would definitely be more accurate. If we were to continue taking our temperature, we would find a lot more data to be within the normal range, and although we might still find outliers, they would be few and far between. As we discussed in class on January 18th, in taking the mean, each data point is given equal value. Therefore, the fewer data points, the more weight each point is given. If more data were to be taken, each point would hold less weight, and therefore outliers would not change the mean quite as much.

Take the arithmetic average of your body temperature and tell me what it is in Celsius. Tell me how you turn Fahrenheit into Celsius.

Fahrenheit is changed to Celsius by taking the Fahrenheit minus 32, and dividing that answer by 1.8.

Carolyn:

(97.817-32)/1.8 = 36.565 C

Kate:

(98.0667-32)/1.8 = 36.704 C

Mean: 97.817

Median: 98.000

Mode: 98.100

Standard Deviation: 0.651

Variance: 0.426

Carolyn’s Stats from SPSS:

Mean: 97.81714

Median: 98.00000

Mode: 98.10000

Standard Deviation: 0.651462

Variance: 0.424403

Kate’s Statistics from Calculator:

Mean: 98.0667

Median: 98.2

Mode: 98.2, 98.5

Standard Deviation: .518

Variance: .268

Kate’s Statistics from SPSS:

Mean: 98.0667

Median: 98.2

Mode: 98.2

Standard Deviation: .51781

Variance: .268

2. It is never possible to exactly predict the next temperature value, or in fact correctly predict any future event. Each time that the temperature is taken, it is a random event. There are many factors that play into what a person’s body temperature will be, and therefore it would be impossible to correctly guess the temperature, just as it would be impossible to guess the IQ of the next baby born.

3. Systematic events present in our data were difficult to find, but when looking closely at the data, one can see that temperatures are lower in the morning and evening, and seem to peak in the afternoon. Temperatures were higher after periods of exercise, and lower after periods of being in cold weather.

4. 7 sources of random variation that affect my life are…

1–Mood, which is affected by many different things, but has a major impact on my day

2–The availability of parking spots, which is also affected by many different things, but can also impact my day

3–Wellness, again, affected by many different things, but being sick would definitely impact a day

4–Weather, cannot be predicted but affects what clothing is worn, what activities can be done

5–Traffic, is a random event but can change how one’s day turns out

6–Interactions with people, vary very much from day to day, but can affect how one feels throughout the day

7–The moods of other people, are random and will affect your mood

5. Sources used:

–WebMD Article on Body Temperature

–Class Lectures

This graph represents the variance in temperature each two hours over a period of five days. Kate’s graph is on the left, and Carolyn’s graph is on the right.