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Geographical Analysis (Oct. 2006) published a study of a new method for analyzing remote-sensing data from satellite pixels in order to identify urban

Analyzing functions
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asked 2020-11-23

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 \(\bar{x}=225\ and\ s=20s=20\). 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 \(\alpha=0.10\). Test for One Standard Deviation Method Null hypothesis \(\Sigma = 22\) Method Alternative hypothesis \(\Sigma = < 22\) The standard method is only for the normal distribution. Statistics NStDevVariance 10020.0400 Tests

Answers (1)

2020-11-24

(a)\(H_{0 }:q = 22,\ H_{a}:q< 22\)

(b)\(P = 0.105\), there is a 10.5% chance of obtaining \(\ll\) sample standard deviation of 20 or more extreme (among 100 observations), when the ture standard deviation is less than 22. There is not sufficient evidence to support the claim that the standard deviation of all grassland pixels is less than 22.

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