Specifics of the Assignment February 4, 2008

Ms. Williams Example

The maximum amount of times that you can have 3 boys in a row out of 100 is 25 times. In Melanie’s data, 3 boys occurred in a row 3 times so she did 3 divided by 25 to get the probability of having 3 boys in succession which equaled 12%. In Danielle’s data, 3 boys occurred in a row one time so she did 1/25 which equaled 4%. Melanie’s data showed a proportion of 53 girls to 47 boys and Danielle’s data showed a proportion of 60 girls to 40 boys. If we generated this 9,900 more times the proportion of boys to girls should get closer and closer to 50/50. This is because larger sample sizes tend to balance out.

A Real Life Example of How the Law of Large Numbers Can Affect You

If I want to know how I’ve done on 100 test scores but I instead choose randomly and only look at five test scores, then my average will most likely be too high or too low, misleading, and not a clear representation of the sample. Of the 3 test scores that I choose randomly, 3 of them might be the only failing grades that I’ve gotten. However, if I look at all 100 test scores, the larger set of the numbers will balance it out.

Male Psychology Majors Example

The proportion of males to females in our statistics class is 8 boys to 38 girls. The percentage of boys in our class is 17.4 %. The percentage male psychology majors nationwide is 25 % (2005). There is a discrepancy due to the fact that our class is a much smaller sample size and also because we go to a University that has a higher proportion of females than males.

Oil Example

Mean= 3258 miles and the SD= 223. We waited until 3,467 miles until we changed the oil which falls below one standard deviation above the mean. Therefore we did not really wait all that long.

The Five Parts of the Weekly Assignment February 4, 2008

Assignment Three: Estimation and the Law of Large Numbers

1. Law of Large Numbers- the theorem that, as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean (2008). Therefore, when taking a collection of random events, it is better to take a larger sample than a smaller one since a larger sample will show less variability. In a small sample size there may be extreme samples that cause the data to be misleading.

The normal frequency distribution (probability distribution) can be used to estimate the likelihood of events occuring in real life so it was used in this lab to estimate the probabilities of random events occuring. The normal curve is a model or theoretical, which will be used to estimate empirical things or real things occuring in the world (MacEwen, 2008).

2. Relate topic to class:

This assignment deals with random events that if measured in a large sample tend to balance out, whereas if a small sample is measured, it can be misleading. The random data in this lab can also be fit by a normal curve model to find probablilties of events occuring.

3. Data:

Ms. Williams data:

To collect this data, we used the random number generator on ourTI-83 plus calculator. 0= girl, 1=boy.

Melanie:

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

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

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

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

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

Danielle:

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

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

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

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

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

** see specifics of the lab for the rest of the data for this example**

4. Sources:

Baily, M. (2005) General verses gender-specific attributes of the psychology major. Journal of General Psychology.
http://209.85.165.104/search?q=cache:K0kD13fts1XOJ:www.encyclopedia.com/doc/1G1-13

Law of large numbers. (2008). In Encyclopedia Britannica. Retrieved February 3, 2008, from Encyclopedia Britannica Online: http://www.britannica.com/eb/article-9384410

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

Pictures came from Google images

5. Strengths/Weaknesses:

The calculator was a strength for this lab because it was very fast in calculating how many boys and girls there would be out of 100. A weakness is that we had to transfer our data from the calculator to our blog and that took a lot of time. It could also be very easy to make a mistake while doing this.

What does this all mean… January 28, 2008

In this lab, our mean temperature was the measurement of central tendency calculated by adding up all the temperatures and diving by 35, which is the number of times we took our temperature. The median temperature was found by writing our temperatures in order from smallest to largest and finding the value in the center of the data. Our mode temperature was the one that was acquired most often in the five day time period. We also found the standard deviation and variance of our temperatures. The standard deviation is the average amount that our temperatures deviated from our mean temperature. The standard deviation helps us determine if our next body temperature will be higher or lower than the mean. The variance also helps us determine how much our temperatures deviated from the mean, however this value is not square rooted.

(Done by Danielle and Melanie)

Answers to Specifics of the Assignment January 28, 2008

• Of the three measures of central tendency, the mean is most influenced by extreme temperature values. If one day you had a fever of 101 degrees F, it would shift your average a few degrees higher. For example, if your average body temperature is 98.7 degrees F and one day you take your temperature and the thermometer says 101 degrees F, your average body temperature would then be 99.85 degrees F. However, if your temperature was only 98.9 degrees F then it would only affect your mean temperature by .1 degree.
• It’s not really rare or unusual to have extremely low or high body temperatures. There are a lot of things that affect your daily temperature and that can throw it off balance such as the weather outside, a hot shower, or getting sick. It may not always be wise to rely on a thermometer reading that shows a very high or very low temperature if you are using it to judge whether or not you are sick because there are many things that can be causing your temperature to be so extreme.
• Most people believe that the average body temperature is 98.6 degrees F, however, this value is incorrect. According to Allen Shoemaker the normal body temperature is 98.25 degrees F. The reason why they came up with the number 98.6 is because of problems with Wunderlich’s original methodology and unreliable thermometers.

D: 98.25-98.1757= 0.0843

M: 98.25-97.3743=0.8757

• Danielle’s average body temperature of 98.1757 is not unusual because it falls within one standard deviation above the mean. Melanie’s average body temperature of 97.3743 is a little bit unusual because it falls between 1 and 2 standard deviations below the mean. Melanie’s is so low due to the fact that she swims in a pool that is much cooler than her body temperature for about 4 hours a day.

• In order to see if our mean body temperatures are good representations we would need more data. If we took our temperatures throughout the semester our means would become more accurate because it would be warmer outside and Melanie’s swimming season would be over.
• In order to change your arithmetic average of your body temperature into Celsius you would use the equation:
  C = (degrees F – 32) * 5/9)

D’s arithmetic mean= 36.76 degrees C

M’s arithmetic mean= 36.32 degrees C

(Done by Danielle and Melanie)

The Five Parts of the Weekly Assignment January 28, 2008

1) Central tendency is the main focus of this lab. Central tendencies are measures of the location of the middle or the center of a distribution. The three measures of central tendency are mean, median, and mode. The mean is the average of a set of data and the most representative of the data points in that it is the value that is closest to all other values in the data set, the median is the middle number of a set of data, and the mode is the most frequently occurring number in a set of data.

Standard deviation and variance are measures of variability. The standard deviation is the arithmetic average deviation of the data points from the mean. The variance is how much the data values deviate from the mean of the whole set of data values.

2) Although body temperature is random and difficult to predict, finding your average body temperature can help you to make the best possible guess. So by looking at a normal distribution of your body temperatures, it can provide a way to compare your temperature to what your average is.

3) Danielle’s 3 Measures of Central Tendency, Variance, and Standard Deviation (according to SPSS):

Mean: 98.1657

Median: 98.1000

Mode: 97.90

Variance: .435

Standard Deviation: .65974

Melanie’s 3 Measures of Central Tendency, Variance, and Standard Deviation (according to SPSS):

Mean: 97.3743

Median: 97.3000

Mode: 97.20

Variance: .231

Standard Deviation: .48102

When using our calculators… The mean, median, and mode for both of us were the same values as calculated in SPSS however both of our standard deviations and variances were off by very little and close enough. Danielle’s standard deviation came to .67 and Melanie’s standard deviation came to .49.

Danielle’s Probability Distribution

Melanie’s Probability Distribution

4)References:

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

MacEwen, B. Spring 2008. January 16, 2008. Psychology 261. Class Lectures. University of Mary Washington.

5)Strengths and Weaknesses

• Strengths in this assignment were that SPSS was very accurate in calculating the mean, median, mode, standard deviation, and variance of our temperatures. When using SPSS it is very easy and you don’t have to worry about making mistakes besides the possibly of entering data in wrong. Another strength in this lab is that we are both female, the same age, and used the same brand of thermometer to take our temperature. Therefore, this eliminated many extra variables that can effect the variation in temperature.
• Weaknesses in this assignment were that errors could be made when calculating the measures of central tendencies on our calculators. This is because it is easy to type a temperature in wrong or make other errors while doing calculations.

(Done by Danielle and Melanie)

January 22, 2008

Answers to questions 4 and 5

4) MacEwen, B. Spring 2008. January 16, 2008. Psychology 261. Class Lectures. University of Mary Washington.

5) List of weaknesses or limitations in the statistics:

• Lack of constant environment, temperature taken inconsistently, inexpensive thermometers

List of strengths or power of the statistics:

• Both female, both live on campus, same age, same thermometer used

After doing this lab we noticed there were strengths and weaknesses in the statistics related to the data collection and the weekly topic of randomness. A few weaknesses that we noticed in the statistics were lack of constant environment, temperature taken inconsistently, and inexpensive thermometers. There was lack of a constant environment while doing this lab since we were not always in our room or in the same place each time we took our temperature. This lack in constant environment while taking our temperature was a result of our schedules since we had to take our temperature in between classes or wherever we were at the time. Another weakness was temperature taken inconsistently since it was difficult because of classes or other activities to take our temperature at exactly 2 hours apart. For example, Melanie had a swim meet on Saturday and it was difficult to take her temperature in between swimming races so temperatures were taken farther apart that day. A third weakness we noticed was inexpensive thermometers. Our thermometers cost about eight dollars, so they are not the most expensive technology to measure temperature. Therefore, the thermometers may have showed weakness in accuracy.

A few strengths we noticed after doing this lab were that we have similarities between us, such as we are both female, the same age, we both live on campus, and we used the same thermometer. Our graphs were both variable and somewhat similar possibly as a result of the things we have in common. A major difference between us however, would be that Melanie swims so that may make her temperature vary more.

January 22, 2008

Melanie’s Hourly Body Temp

3b)Danielle’s Hourly Body Temp

Melanie’s mean: 97.37 Danielle’s mean:98.17

3) Q: Are there any systematic effects present in our data?

After Melanie warmed up for swim practice her temperature would always be the highest. Also for both of us, when we would take our temperature after having just walked outside it would be very low. Our temperature was always colder in the morning for both of us because we dont put the heat on in the room over night. After drinking hot chocolate my temperature was very high.

Seven Other Sources of Variation

1. Sickness can have an affect on our daily lives. It can cause you to miss a test or it can put you in the hospital.

2. A death of a loved one can cause depression and make you miss work.

3. The weather can affect your mood and affect how quickly you can get around. A hurricane can drastically affect your life.

4. A very important exam that determines whether or not you pass a class.

5. A stressful job

6. Giving birth to a baby and finding out that they have a disability.

7. Coming home to your house that has been ransacked and robbed.

 

Questions 1 & 2 January 10, 2008

1) Q: What is meant by a “random event” and how does it differ from a “systematic event”?

A random event is impossible to predict due to the fact that there are too many unpredictable factors that influence its occurence that we cannot know in advance. A systematic event is one that is created by bias.

2) Q: Is it possible to predict correctly any future event?

It is possible to predict a future event. If you did accurately guess, it would be because of chance. If you wanted to guess what your temperature would be the next time you take it, take your temperature a few times a day and then find your mean or average temperature. By guessing your mean body temperature, you are more likely to at least be close.