An insurance company selected a random sample of 380 automobile accident reports. Each report was classified...

  

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An insurance company selected a random sample of 380 automobile accident reports. Each report was classified by size of automobile (large or small) and whether or not any of the occupants were killed. The data are shown below, Size of Automobile Small Large Fatal 39 21 Not fatal 181 139 Total 220 160 Call ps the proportion of all accidents involving small cars in which there is a fatality and pL the corresponding proportion for large automobiles. (a) Compute the corresponding sample proportions ps and pL. Write a couple of sentences comparing these two values. (b) What is the difference in accident rates, ps- pL? (c) Compute the overall (pooled) sample proportion of accidents that are fatal, regardless of size. (b) What is the difference in accident rates, ps - pL? (c) Compute the overall (pooled) sample proportion of accidents that are fatal, regardless of size. (d) Compute the standard error (SE) of the sample difference (ps - pt.) assuming we want to test a hypothesis about ps - PL. (e) Verify that the "success/failure" conditions are met. () Compute the Z-value for a two-sample Z-test. (g) Compute the p-value for testing whether the fatality rate for accidents involving small automobiles exceeds that for large cars. (h) Write a conclusion for this test. () In reaching your conclusion in Part (h), which hypothesis testing error might you have made? Please give your answer in the context of the data. An insurance company selected a random sample of 380 automobile accident reports. Each report was classified by size of automobile (large or small) and whether or not any of the occupants were killed. The data are shown below, Size of Automobile Small Large Fatal 39 21 Not fatal 181 139 Total 220 160 Call ps the proportion of all accidents involving small cars in which there is a fatality and pL the corresponding proportion for large automobiles. (a) Compute the corresponding sample proportions ps and pL. Write a couple of sentences comparing these two values. (b) What is the difference in accident rates, ps- pL? (c) Compute the overall (pooled) sample proportion of accidents that are fatal, regardless of size. (b) What is the difference in accident rates, ps - pL? (c) Compute the overall (pooled) sample proportion of accidents that are fatal, regardless of size. (d) Compute the standard error (SE) of the sample difference (ps - pt.) assuming we want to test a hypothesis about ps - PL. (e) Verify that the "success/failure" conditions are met. () Compute the Z-value for a two-sample Z-test. (g) Compute the p-value for testing whether the fatality rate for accidents involving small automobiles exceeds that for large cars. (h) Write a conclusion for this test. () In reaching your conclusion in Part (h), which hypothesis testing error might you have made? Please give your answer in the context of the data.

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