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IT 223 -- Project 2

Part A: Analyzing a Univariate Dataset

• Collect a univariate dataset containing at least 15 observations that follows the ideal measurement model:
  Actual measurement = true measurement + random error

• Here are some suggestions:
  Time for a cup of water to boil on a stove

  Time for your dog to come to you when you call it

  Time to go to work over the same route

  Time for a Red Line train to travel from the Fullerton stop to the Jackson stop

  Time for an email message sent to yourself to arrive

  Number of words on random pages of a book that does not contain figures or tables

  Number of words in newspaper articles

  Your pulse rate measured at random times during the day

  Your weight measured at random times during the day

  Weight of of a packages of meat at a store of approximately the same weight (you may need to go to more than one store)

  Weight of each potato in a 10 pound bag

  Lengths of "30 second" television commercials in seconds

  Newspaper prices of used cars, which are of the same make and model

  Heights of persons of the same gender in this class

  The roundtrip ping time for an IP packet

  The number of time for a spring loaded kitchen timer to "time" 30 seconds.
  Because of random error, there may be more variation than you think.

• Then use SPSS to answer these questions. Type the answers to the starred questions at the top of your SPSS output file (.docx file type). Also make sure that your name is shown at the top of your submission as well as in the filename.

• Important:   Do not sort the data before performing the analyses.
  1. *Describe your dataset and the circumstances under which you collected the data.

  2. Print your dataset.

  3. *What are Q0, Q1, Q2, Q3, and Q4?

  4. *What are the sample mean and standard deviation?

  5. Use SPSS to plot histograms with three different interval widths.

  6. *Use SPSS to plot a boxplot. What does the boxplot tell you?

  7. *List any moderate or extreme outliers using the boxplot. See Hint 1 below.

  8. Create a new column of z-scores in the dataset. See the Transform Variables section of the Brief SPSS Tutorial. Print the z-scores.

  9. *List any moderate or extreme outliers using z-scores. See Hint 2 below.

  10. *Plot your dataset by observation number. Describe this plot using the terms unbiased, biased, homoschedastic, and heteroscedastic. Can you think of any "lurking variables" that might cause your dataset to deviate from an ideal measurement model? A lurking variable is a variable not included in the dataset that might affect the results.

Hints:

1. To find outliers using Q1, Q3, and IQR:
   An extreme outlier is a data point that is more than 3 IQRs below Q1 or more than 3 IQRs above Q3.

   An extreme outlier is a data point that is more than 1.5 IQRs below Q1 or more than 1.5 IQRs above Q3, and is not an extreme outlier.

2. To find outliers using z-scores:
   An extreme outlier is a data point that has a z-score of more than 3 or less than -3.

   An mild outlier is a data point that has a z-score greater than 2 or less than -2, and is not an extreme outlier.

3. To plot the dataset by observation number:
   1. Create the scatterplot of the datapoints (y-axis) vs. the observation number (x-axis), select Graphs >> Interactive >> Scatterplot. Drag the y-variable into the box with the vertical arrow through it. Drag the observation number variable into the box with the horizontal arrow though it. Click OK.

Part B: Random Number Simulations

• Perform two simulations with random numbers to see how the normal plots behave:
  1. To create a dataset consisting of 100 normal random numbers with center 5 and spread 3:
     1. Type in using the data editor, a variable that represents the observation number called Number or ObsNum. Cut and paste from Excel to speed up the data entry process.

     2. Select Transform >> Compute Variable. Enter x in the Target Variable box and and Rv.Normal(5, 3) as the expression to compute. Click Ok

     3. Compute the normal plot as you did in Problem 7 of Part A.

  2. To create a dataset consisting of 100 uniform random numbers, repeat the steps in 1, except use Rv.Uniform(2, 4) as the expression to compute.

Part C: Probabilities for Normal Distribution

• Use SPSS to help you solve the following problems. Show a printout of your SPSS datasets containing the calculated variables in your output. Check your answers with the normal and extreme normal tables from the textbook. Copies of these tables are also on the Documents Page.

  Use the SPSS function Cdf.Normal(z,0,1) to find the area of the standard normal curve for the interval (-∞, z]. Use Idf.Normal(p,0,1) to find the z for which the area of (-∞, z] is p.

  1. LSAT scores are normally distributed with mean 150 and SD 10. What percentage of students taking the LSAT test obtain a score
     1. under 142?

     2. over 191?

     3. between 153 and 174?

  2. Horse pregnancies are normally distributed with mean 336 days and SD 3 days. What percent of horse pregnancies are between 335 and 338 days?

  3. Determine the following percentiles for LSAT scores (see Problem A1):
     a. 57      b. 98      c. 39

  4. Determine the following percentiles for horse pregnancies:
     a. 89      b. 45