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Warm-Up: Check Your Understanding Fill in the blank with the name of the most appropriate Chi-
square test to address the research questic 1. A researcher wants to determine if scoring high or
low on an artistic ability test depends on be right or left-handed. Answer: Chi-Square test of 2. A
national organization wants to compare the distribution of level of highest education complet (high
school, college, masters, doctoral) for Republicans versus Democrats. Answer: Chi-Square test of
3. A preservation society has the percentages of five main types of fish in the river from 10 years a
After noticing an imbalance recently, they add some fish from hatcheries to the river. How can t
determine if they restored the ecosystem from a new sample of fish? Answer: Chi-Square test
ofILP: Is There a Different Pattern in the Distribution of Accidental Deaths in a Certain Region
Compared to the Pattern in the Entire United States? Background: According to the records of the
National Safety Council, accidental deaths in the United States during 2002 had the following
distribution according to the principal types of accidents. Suppose that an accidental death data
set from a particular geographical region yielded the following frequency distribution for the
principal types of accidents: Do these data show a significantly different pattern in the distribution
of accidental deaths in the particular region compared to the pattern in the entire United States?
Use a 5% significance level. (Source: National Safety Council Website, 2005) Task: Perform a
Chi-square goodness of fit test to assess whether the data fit well with the model specified in the
null hypothesis. 1. State the null hypothesis: Determine Alpha: We were told to use a significance
level of 5%.2. Checking the Assumptions a. Find the expected counts and fill them in the table
below. b. Do all cells have expected counts greater than 5 ? Yes No 3. Compute the Test Statistic
and Calculate the p-value Test-Statistic a. Complete the calculation of the test statistic based on
your table above by calculating the contribution of "other" accidental deaths to the total test
statistic. X2=445.5(442445.5)2+148.5(161148.5)2+39.6(4239.6)2+29.7(3329.7)2+158.4(162158.4
)2+(..)2=3.663Calculate the p-Value: b. Based on the output below, answer the following: i. The p-
value is ii. The expected value of the test statistic assuming H0 is true is iii. The large p-value we
obtained is consistent with the fact that our observed test statistic value is greater than less than
the expected test statistic value (under the null hypothesis). 4. Evaluate the p-value and
Conclusion: Evaluate the p-value: What is your decision at a 5% significance level? Reject H0 Fail
to Reject H0 Remember: Reject H0 Results statistically significant Fail to Reject H0 Results not
statistically significant Conclusion: What is your conclusion in the context of the problem?

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  • 1. Warm-Up: Check Your Understanding Fill in the blank with the name of the most appropriate Chi- square test to address the research questic 1. A researcher wants to determine if scoring high or low on an artistic ability test depends on be right or left-handed. Answer: Chi-Square test of 2. A national organization wants to compare the distribution of level of highest education complet (high school, college, masters, doctoral) for Republicans versus Democrats. Answer: Chi-Square test of 3. A preservation society has the percentages of five main types of fish in the river from 10 years a After noticing an imbalance recently, they add some fish from hatcheries to the river. How can t determine if they restored the ecosystem from a new sample of fish? Answer: Chi-Square test ofILP: Is There a Different Pattern in the Distribution of Accidental Deaths in a Certain Region Compared to the Pattern in the Entire United States? Background: According to the records of the National Safety Council, accidental deaths in the United States during 2002 had the following distribution according to the principal types of accidents. Suppose that an accidental death data set from a particular geographical region yielded the following frequency distribution for the principal types of accidents: Do these data show a significantly different pattern in the distribution of accidental deaths in the particular region compared to the pattern in the entire United States? Use a 5% significance level. (Source: National Safety Council Website, 2005) Task: Perform a Chi-square goodness of fit test to assess whether the data fit well with the model specified in the null hypothesis. 1. State the null hypothesis: Determine Alpha: We were told to use a significance level of 5%.2. Checking the Assumptions a. Find the expected counts and fill them in the table below. b. Do all cells have expected counts greater than 5 ? Yes No 3. Compute the Test Statistic and Calculate the p-value Test-Statistic a. Complete the calculation of the test statistic based on your table above by calculating the contribution of "other" accidental deaths to the total test statistic. X2=445.5(442445.5)2+148.5(161148.5)2+39.6(4239.6)2+29.7(3329.7)2+158.4(162158.4 )2+(..)2=3.663Calculate the p-Value: b. Based on the output below, answer the following: i. The p- value is ii. The expected value of the test statistic assuming H0 is true is iii. The large p-value we obtained is consistent with the fact that our observed test statistic value is greater than less than the expected test statistic value (under the null hypothesis). 4. Evaluate the p-value and Conclusion: Evaluate the p-value: What is your decision at a 5% significance level? Reject H0 Fail to Reject H0 Remember: Reject H0 Results statistically significant Fail to Reject H0 Results not statistically significant Conclusion: What is your conclusion in the context of the problem?