CSCI A113 Practice Problems First semester 2000-2001

1. BASIC CHARTS

1. Open a new workbook. Type Year in cell A1 and enter the years 1991 through 1994 in cells A2:A5. Type Sales in cell B1 and enter 135, 201, 174, and 238 in cells B2:B5. These sales figures are in thousands of dollars. Select cells B2:B5, click the Currency Style button (icon $), and click the Decrease Decimal button twice. Prepare a column chart (vertical bars) showing Year on the horizontal axis and Sales on the vertical axis.

2. Enter the year and sales data as described in the exercise above. Prepare a bar chart (horizontal bars) with Year on the vertical axis (1991 on top and 1994 on the bottom) and Sales on the horizontal axis.

3. Enter the year and sales data as described in the first exercise. Prepare a pie chart showing annual sales as a proportion of total sales during the four-year period.

4. Enter the year and sales data as described in exercise 1.1 above. Prepare a line chart showing Year on the horizontal axis and Sales on the vertical axis.

2. UNIVARIATE NUMERICAL DATA

1. Construct a frequency distribution and histogram for the following selling prices of 15 properties:

   $26,000    $38,000    $43,600
    31,000     39,600     44,800
    37,400     31,200     40,600
    34,800     37,200     41,800
    39,200     38,400     45,200

   Use intervals $5,000 wide starting at $25,000. Comment on the symmetry or skewness of the selling prices.

2. Determine measures of central tendency and dispersion for the selling prices of the 15 properties in the exercise above. Which measure(s) of central tendency should be used to describe a typical selling price? What is the mode or modal interval?

3. To verify the symmetry or skewness observed in exercise 2.1 above, calculate Pearson's coefficient of skewness.

3. BIVARIATE NUMERICAL DATA

1. An economist wanted to determine how office vacancy rates depend on average rent. She took a random sample of the monthly office rents per square foot and the percentage of vacant office space in ten different cities. The results are shown in the following table.

               Vacancy       Monthly Rent
     City      Percentage    per Sq. Ft. 
     
      1           3             $5.00
      2          11              2.50
      3           6              4.75
      4           5              4.50
      5           9              3.00
      6           2              4.50
      7           5              4.00
      8           7              3.00
      9          10              3.25
     10           8              2.75

   Arrange the data in appropriate columns and prepare a scatterplot. Does there appear to be a positive or negative relationship between the two variables?

2. Compute the correlation coefficient for the data in the exercise above. Comment on the direction and strength of the linear relationship.

3. Does a student's test grade seem to depend on the number of hours spent studying? The following table shows the number of hours 20 students reported studying for a major test and their test grades.

             Study   Test                       Study   Test
   Student   Hours   Grade            Student   Hours   Grade 
   
      1        5      54                11       12      74
      2       10      56                12       20      78
      3        4      63                13       16      83
      4        8      64                14       14      86
      5       12      62                15       22      83
      6        9      61                16       18      81
      7       10      63                17       30      88
      8       12      73                18       21      87
      9       15      78                19       28      89
     10       12      72                20       24      93

   Arrange the data in the appropriate columns and prepare a scatterplot. Does there appear to be a positive or negative relationship between the two variables?

4. Compute the correlation coefficient for the data in exercise 3.3 above. Comment on the direction and strength of the linear relationship.

4. SIMPLE LINEAR REGRESSION

1. Refer to the data on vacancy percentages and monthly rents for ten cities in exercise 3.1 above.
   1. Prepare a scatterplot and insert a linear trendline.
   2. Use the Regression analysis tool to obtain complete diagnostics.
   3. Make a prediction of vacancy percentage for a city where monthly rent per square foot is $3.50.

2. Refer to the data on study hours and test grades for 20 students in exercise 3.3 above.
   1. Prepare a scatterplot and insert a linear trendline.
   2. Use the Regression analysis tool to obtain complete diagnostics.
   3. Make a prediction of test grade for a student who studies ten hours.
   4. Student 7 studied ten hours and received a test grade of 63. Taking into account the number of study hours, is this test grade below average, average, or above average?