Geographical Analysis (Oct. 2006) published a study of a new method for analyzing remote-sensing data from satellite pixels in order to identify urban land cover. The method uses a numerical measure of the distribution of gaps, or the sizes of holes, in the pixel, called lacunarity. Summary statistics for the lacunarity measurements in a sample of 100 grassland pixels are xÌ… = 225 and s = 20. It is known that the mean lacunarity measurement for all grassland pixels is 220. The method will be effective in identifying land cover if the standard deviation of the measurements is 10% (or less) of the true mean (i.e., if the standard deviation is less than 22).
a. Give the null and alternative hypotheses for a test to determine whether, in fact, the standard deviation of all grassland pixels is less than 22.
b. A MINITAB analysis of the data is provided below. Locate and interpret the p-value of the test. Use a = .10.

Transcribed Image Text:

Test for One Standard Deviation Method Null hypothesis Alternative hypothesis Sigma = < 22 Sigma - 22 The standard method is only for the normal distribution. Statistics N StDev Variance 100 20.0 400 Tests Method Chi-Square DF P-Value 81.82 99 0. 105 Standard