Refer to the Geographical Analysis (Oct. 2006) study of a new method for analyzing remote-sensing data from satellite pixels, presented in Exercise 8.32 (p. 365). Recall that 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 x = 225 and s = 20. As stated in Exercise 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 hypothesis 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 on page 400. Locate and interpret the p -value of the test. Use α = .10.