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The number of AIDS cases reported in a particular county is broken down by race in the table below. Race Cases White 2177 1178 450 222 4027 Hispanic Black Asian/Pacific Islander Total

The number of AIDS cases reported in a particular county is broken down by race in the table below. Race Cases White 2177 1178 450 222 4027 Hispanic Black Asian/Pacific Islander Total

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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The number of AIDS cases reported in a particular county is broken down by race in the table below. Race Cases White 2177 1178 450 222 4027 Hispanic Black Asian/Pacific Islander Total Directions: Conduct a chi-square test for goodness-of-fit to determine whether or not the occurrence of AIDS cases is consistent with the race distribution in a particular county. 1. Choose the correct null and alternative hypotheses. O Ho The distribution of AIDS cases is different from the race distribution in a particular county. Ha: The distribution of AIDS cases is consistent with the race distribution in a particular county. O Ho: The distribution of AIDS cases is consistent with the race distribution in a particular county. Ha The distribution of AIDS cases is different from the race distribution in a particular county. 2. Compute the test statistic. The population distribution in a particular county by race is provided in the table below. Use these percentages to compute the expected number of cases for each racial group. Round each of the expected counts to 2 decimal places. Race White Hispanic Black Asian/Pacific Islander Total x²: = Proportion 0.425 0.282 p-value = 0.027 0.266 Determine the value of the test statistic. Round your answer to 1 decimal place. 1 Expected cases 3. Compute the p-value. Round your answer t 4 decimal places. 4. Interpret the results of the significance test. O The differences between the distribution of AIDS cases and the distribution of the general population in a particular county are not statistically significant. From a practical perspective, the differences are minor. O The differences between the distribution of AIDS cases and the distribution of the general population in a particular county is statistically significant. The differences are also important from a practical perspective. For example, the number of blacks with AIDS is 3.1 times more than expected and the number of Asian/Pacific Islanders with AIDS is 3.8 times less than expected.
Transcribed Image Text:The number of AIDS cases reported in a particular county is broken down by race in the table below. Race Cases White 2177 1178 450 222 4027 Hispanic Black Asian/Pacific Islander Total Directions: Conduct a chi-square test for goodness-of-fit to determine whether or not the occurrence of AIDS cases is consistent with the race distribution in a particular county. 1. Choose the correct null and alternative hypotheses. O Ho The distribution of AIDS cases is different from the race distribution in a particular county. Ha: The distribution of AIDS cases is consistent with the race distribution in a particular county. O Ho: The distribution of AIDS cases is consistent with the race distribution in a particular county. Ha The distribution of AIDS cases is different from the race distribution in a particular county. 2. Compute the test statistic. The population distribution in a particular county by race is provided in the table below. Use these percentages to compute the expected number of cases for each racial group. Round each of the expected counts to 2 decimal places. Race White Hispanic Black Asian/Pacific Islander Total x²: = Proportion 0.425 0.282 p-value = 0.027 0.266 Determine the value of the test statistic. Round your answer to 1 decimal place. 1 Expected cases 3. Compute the p-value. Round your answer t 4 decimal places. 4. Interpret the results of the significance test. O The differences between the distribution of AIDS cases and the distribution of the general population in a particular county are not statistically significant. From a practical perspective, the differences are minor. O The differences between the distribution of AIDS cases and the distribution of the general population in a particular county is statistically significant. The differences are also important from a practical perspective. For example, the number of blacks with AIDS is 3.1 times more than expected and the number of Asian/Pacific Islanders with AIDS is 3.8 times less than expected.
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