GEOG 090 – Spring 2005

Assignment #4 – Sampling, Confidence Intervals, and Hypothesis Testing

Due: Thursday, March 24, 2005 at the beginning of class

  1. Follow the instructions for Question 6 on pages 63-64 of Rogerson, as specified in the text. The requested sampling approaches require you to generate random numbers in pairs in order to select x and y coordinates to sample elevations on the contour map. You may use Table A.1 on pages 212-213 to generate random numbers (see the top of page 58 for an explanation of how to do this, and keep in mind we want to generate values between 0-100, not 1-20), or use this linked Excel workbook that is set up to generate pairs of random numbers between 0-100 using the RANDBETWEEN function (simply change any cell in the worksheet to get a new pair of random numbers). The contour map is conveniently set up with 0-100 coordinates marked on each axis. Translate the random number pairs to positions on the contour map with the help of ruler.

Find the elevation at a point on the map by noting which pair of contour lines the point is between (there are 30, 40, 50, 60, and 70 units of elevation contour lines on the map) and assume constant slope between the contour lines (i.e. a point halfway beween the 40 and 50 unit lines is at 45 units of elevation, and since there is no 80 unit line on the map, assume a point within the 70 unit contour can be no higher than 75 units of elevation, points between the 50 unit line and the boundary in the southwest corner have an elevation no lower than 45 units, and points between the 30 unit line and the boundary in the northeast corner have an elevation no lower than 25 units). To help you in your sampling tasks, I have provided copies of the contour map you will be sampling: that are conveniently scaled for use with a metric ruler:

(a)

(b)

(c)

Show your work in the assignment you submit by including:

  • 3 contour maps annotated with the locations of your sample points
  • 3 tables that show the (x,y) coordinates of the sample points you randomly selected and the elevation values at each point
  • The 3 mean elevation estimates you calculate from the samples

  1. Follow the instructions for Question 7 on page 40 of Rogerson, as specified in the text.
  1. Follow the instructions for Question 1 on page 62 of Rogerson, as specified in the text. Formulate the test statistic as described on page 48 (equation 3.10) to yield a z-score, and then look up the probability associated with the z-score value to find the p-value at which this sample can be used to reject the null hypothesis. Be sure to report the p-value, and to comment on whether her sample is sufficient evidence to support her hypothesis.

The sample mean here is calculated by dividing the number of professors who voted for candidate A by the total number sampled (i.e. p = 20/45), and the population mean (the statewide percentage of the population voting for Candidate A) was given. Estimate the population standard deviation using the sample, using the formula s = [(p)(1-p)] (this is precisely equivalent to calculating a population standard deviation using 20 values of 1 and 25 values of 0, but this way saves a lot of work).

Format for answering questions in GEOG 090

1.Show all of your work in a neat, organized fashion.

2.If numbers are to be plugged into a formula, write out the formula first.

3.Provide the units of a final answer if applicable.

4.Final numerical answers should be circled for easy identification

5.Graphs should be large enough to discern - make liberal use of graph paper.

6.Graphs, tables should have a title and legend (if there is more than one variable portrayed).

7.Axes on graphs should be labeled with the variable name and the units.

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