Lab Activity 5 Math 113 Name : _________________
10 Pts Intro to Applied Stats


  1. Is there a relationship between the length of a person's name and their phone number?
    1. Ask 10 people their last name and the last 4 digits of their phone number. Record the length of their last name (x) and the sum of the last four digits of their phone number (y) in the table.
x                    
y                    
    1. Enter the x values into List 1 and the y values into List 2 on the calculator.
    2. Compute the correlation coefficient r for the data using the command: LinReg(ax+b) L1,L2


    3. Compute the correlation coefficient r if the variables are switched: LinReg(ax+b) L2,L1


    4. Add 10 to every x value and save the results into List 3. L1+10L3 and compute the correlation coefficient with the new x-values and the y-values: LinReg(ax+b) L3,L2


    5. Multiply every y value by 10 and save the results into List 3. L2*10L3 and compute the correlation coefficient with the original x-values and the new y-values: LinReg(ax+b) L1,L3


    6. Summarize the effect each translation has on the correlation coefficient.
      1. Switching the variables


      2. Adding a constant to one or both variables


      3. Multiplying one or both variables by a constant

  1. Do fatal airplane crashes occur with equal frequency throughout the week?

Data obtained from the National Transportation Safety Board (NTSB) from January 1, 1996 to April 19, 1998 is summarized in the table. The values in the table are the number of fatal airplane crashes occurring on each day of the week. http://www.ntsb.gov/aviation/Accident.htm
Day Sat Sun Mon Tue Wed Thu Fri Total
Accidents 130 109 91 80 87 100 106 703
Expected               703

    1. Complete the table by filling in the expected frequencies.
    2. Test the claim that fatal accidents occur with equal frequency throughout the week.
      1. What requirement must be met to test this claim?


      2. Is it met? (yes / no)
      3. H0: The (observed / expected) frequencies are the same.
      4. H1: At least one (observed / expected) frequency is different.
      5. There are ______ categories, so there are ______ degrees of freedom.
      6. The test statistic will have a _______________ distribution.
      7. The critical value is _____________.
      8. The formula for the test statistic is:


      9. The test statistic is ______________.
      10. The decision is to (reject / fail to reject) the null hypothesis.
      11. There is ____________ evidence at the __________ level of significance to _____________ the claim that fatal accidents occur with equal frequency throughout the week.


    3. Rearrange the data in the table so that the week starts with Sunday instead of Saturday. Recalculate the test statistic.


    4. Multiply every observed and expected frequency by 10. Recalculate the test statistic.


    5. Add 10 to every observed and expected frequency. Recalculate the test statistic.


    6. Summarize the effect of each translation on the test statistic.
      1. Rearranging the order of the categories (cells)


      2. Multiplying all frequencies by a constant


      3. Adding a constant to all the frequencies


  1. Is the number of games won by an NBA team independent of the division they are in? Consider the 1997-98 NBA Regular Season Final Standings shown. The number of games won for the top seven finishers in each division are given. Only the Toronto Raptors in the Central division are omitted. http://www.nba.com/score_stat/standings.html
Place
Division 1 2 3 4 5 6 7 Total
Atlantic 55 43 43 42 41 36 31 291
Central 62 58 51 50 47 37 36 341
Midwest 62 56 45 41 20 19 11 254
Pacific 61 61 56 46 27 19 17 287
Total 240 218 195 179 135 111 95 1173
    1. Enter the 4x7 matrix into your calculator as matrix [A]. Omit the totals when entering the data into the calculator.
    2. Test the claim that the number of games won is independent of the division.
      1. H0: There (is / is not) a relationship between the number of games won and the division.
      2. H1: There (is / is not) a relationship between the number of games won and the division.
      3. There are _______ rows, therefore the degrees of freedom for the rows is _________. (total rows don't count)
      4. There are _______ columns, therefore the degrees of freedom for the columns is ________. (total columns don't count)
      5. This is a _____ x _____ matrix, therefore, the degrees of freedom is ______ x ______ = ________.
      6. The test for independence has a _____________ distribution.
      7. The critical value is ____________.
      8. The formula for the test statistic is:


      9. The test statistic (use your calculator) is ____________.
      10. The decision is to (reject / fail to reject) the null hypothesis.
      11. There is __________ evidence at the __________ level of significance to ____________ the claim that the number of games won is independent of the division.


    3. We are going to be manipulating the data in the matrix. Make a backup copy of the matrix using the command: [A] Sto> [B] (Matrix 1 Store Matrix 2 enter)
    4. Switch the rows and columns in the matrix so that the divisions are the columns and the standings are the rows (it will be a 7x4 matrix). The easiest way to do this is to use the transpose command on the calculator. [B]T Sto> [A] (the transpose T operator is found under Matrix, Math, #2). Recalculate the test statistic.


    5. Re-enter the matrix into your calculator (as a 4x7 matrix) so that the order of the rows is Central, Midwest, Pacific, and Atlantic. Recalculate the test statistic.


    6. Multiply every value in the original matrix by 10 using the calculator command 10*[B] Sto> [A]. Recalculate the test statistic.


    7. Add 10 to every value in the original matrix. You can re-enter these values manually, or create a 4x7 [C] matrix which has 10 in every element and then go [B]+[C] Sto> [A]. Recalculate the test statistic.


    8. Summarize the effect of the following transformations on a contingency table.
      1. The rows and columns variables are interchanged


      2. The order of the rows or the order of the columns are changed


      3. Every value is multiplied by a constant


      4. Every value has a constant added to it