An investigation of all five major fires in a western desert during one of the r

Question

An investigation of all five major fires in a western desert during one of the recent summers found the following causes. Arson Accident Accident Arson Accident a. What proportion of those fires were due to arson? b. How many total samples (without replacement) of size three can be selected from this population? c. List all the possible samples of size three that can be selected from this population and calculate the sample proportion pˆ of the fires due to arson for each sample. Prepare the table that gives the sampling distribution of pˆ. d. For each sample listed in part c, calculate the sampling error.

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Explanation / Answer

Proportion of fires due to arson = 2/5 = 0.4

Total sample of size 3 = 5C3 = 10

Sampling error = population proportion - sample proportion

Sample No Fires chosen Proportion due to arson Sampling error 1 123 1/3 0.07 2 124 2/3 -0.27 3 125 1/3 0.07 4 134 2/3 -0.27 5 135 1/3 0.07 6 145 2/3 -0.27 7 234 1/3 0.07 8 235 0 0.4 9 245 1/3 0.07 10 345 1/3 0.07

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