CS130 Practice Problems

Problem #1:

The harmonic mean of a set of numbers is the number of scores N, divided by the reciprocals of each number. As an example, the harmonic mean of 7,8,7,3,6,2 is:

6 / (1/7 + 1/8 + 1/7 + 1/3 + 1/6 + 1/2) = 4.3

Design an Excel worksheet that allows the user the ability to enter up to 10 numbers and prints the harmonic mean of the numbers entered. Note: The user can enter from 1 and 10 different numbers inclusively.

Here is an example:

Numbers       Reciprocal       Harmonic Mean =  4.253165
      7      0.142857143
      8            0.125
      7      0.142857143
      3      0.333333333
      6      0.166666667
      2              0.5

Make your worksheet look like the following:

Problem #2:

For a random number of selected homes sold in Washington County, the annual tax amount (in thousands of dollars) and selling price (in thousands of dollars) are as follows (do not use this data as an answer in your current homework):

Taxes:  4.0  2.4  1.8  1.5  1.4  1.4  3.0  1.9
Selling
Price:  265  142  114  160  130  150  228  145

a) Perform a Linear Regression on the above data using Excel and SPSS.

b) What is the linear equation produced be performing the Linear Regression?

c) For an annual tax amount of $2,450, what might we expect the selling price of this house to be?

d) For a selling price of $235,000, what might we expect the taxes to be for this house?

Problem #3:

Consider the following two cold medicines tested for acetaminophen. Test the claim that the mean amount of acetaminophen is the same for both medicines. What is your conclusion? Explain. In particular, state your NULL Hypothesis, perform the appropriate Hypothesis test, state your conclusion.

Brand A  472  487  506  512  489  503  511  501  495  504  494  462
Brand B  562  512  523  528  554  513  516  510  524  510  524  508 

Problem #4:

The NCAA is considering ways of speeding up the end of college basketball games. In a recent NCAA tournament, the last two minutes of 60 games took the following times to complete (in seconds):

756  587  929  871  378  503  564 1128  693  748
448  670 1023  335  540  853  852  495  666  474
443  325  514  404  820  915  793  778  627  483
861  337  292 1070  625  457  676  494  420  862
991  615  609  723  794  447  704  396  235  552
626  688  506  700  240  363  860  670  396  345

a) In both Excel and SPSS, find the mean, median, mode, standard deviation, minimum, and maximum values for the given data. Paste these results into a Word document.

b) Create a histogram of the given data.

c) Do these times indicate that something should be done to speed up the last two minutes of the game? Support your answer as best you can.