Chapter 1. Uses of the Chi-Square Test

Correct. Data can be collected in one of three ways for a chi-square test: one simple random sample, two or more simple random samples—one from each population or random allocation of subjects to treatments. However, the response must be categorical.

Incorrect. Data can be collected in one of three ways for a chi-square test: one simple random sample, two or more simple random samples—one from each population or random allocation of subjects to treatments. However, the response must be categorical.

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Correct. The type of data collection does indeed determine the hypotheses.

Incorrect. The type of data collection does indeed determine the hypotheses.

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Correct. All three types of data collection have the same chi-square test statistic.

Incorrect. All three types of data collection have the same chi-square test statistic.

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Correct. Here one simple random sample was taken and students were asked two questions.

Incorrect. Here one simple random sample was taken and students were asked two questions.

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Correct. Here eggs were randomly assigned to one of three temperatures, making this study a completely randomized experiment.

Incorrect. Here eggs were randomly assigned to one of three temperatures, making this study a completely randomized experiment.

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Correct. Here three simple random samples were taken and respondents were asked one question.

Incorrect. Here three simple random samples were taken and respondents were asked one question.

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Correct. For a chi-square test, expected counts must be at least 5. If that condition is not met, then all expected counts need to be greater than 1 and no more than 20% can be less than 5. By the way, we cannot compute standard deviations using categorical data.

Incorrect. For a chi-square test, expected counts must be at least 5. If that condition is not met, then all expected counts need to be greater than 1 and no more than 20% can be less than 5. By the way, we cannot compute standard deviations using categorical data.

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Correct. The three treatments, desipramine, lithium and a placebo, will be compared in this study.

Incorrect. The three treatments, desipramine, lithium and a placebo, will be compared in this study.

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Correct. We use a chi-square test to analyze the results of an experiment when both the response variable and the explanator variable are categorical.

Incorrect. We use a chi-square test to analyze the results of an experiment when both the response variable and the explanator variable are categorical.

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Correct. To test the equality of three proportions, we test H₀: p₁ = p₂ = p₃. The hypothesis, “H₀: Not all proportions are the same”, is a statement of an alternative hypothesis. And we use the symbol, “p” (not “µ”), when testing proportion.

Incorrect. To test the equality of three proportions, we test H₀: p₁ = p₂ = p₃. The hypothesis, “H₀: Not all proportions are the same”, is a statement of an alternative hypothesis. And we use the symbol, “p” (not “µ”), when testing proportion.

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Correct. We need random allocation of patients to treatments so that the experiment will be valid and so that the conditions for performing the chi-square test will be met.

Incorrect. We need random allocation of patients to treatments so that the experiment will be valid and so that the conditions for performing the chi-square test will be met.

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Correct. expected = \(\frac{(row total)(column total)}{table total} \) = \(\frac{(14)(24)}{72} \) = 16

Incorrect. expected = \(\frac{(row total)(column total)}{table total} \) = \(\frac{(14)(24)}{72} \) = 16

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Correct. All expected counts are either 16 or 8 for this study. Both 16 and 8 are greater than 5, so the expected counts are large enough.

Incorrect. All expected counts are either 16 or 8 for this study. Both 16 and 8 are greater than 5, so the expected counts are large enough.

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Correct. The contribution to the chi-square test statistic for the placebo/relapse cell is \(\frac{ (observed-expected)^{2} }{expected} = \frac{ (20-16)^{2} }{16} = 1.00\)

Incorrect. The contribution to the chi-square test statistic for the placebo/relapse cell is \(\frac{ (observed-expected)^{2} }{expected} = \frac{ (20-16)^{2} }{16} = 1.00\)

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Correct. degrees of freedom = (r – 1)(c – 1) = (3 – 1)(2 – 1) = 2

Incorrect. degrees of freedom = (r – 1)(c – 1) = (3 – 1)(2 – 1) = 2

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Correct. Since P-value = 0.0052 is less than α = 0.02, we can reject the null hypothesis.

Incorrect. Since P-value = 0.0052 is less than α = 0.02, we can reject the null hypothesis.

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Correct. Yes, we can conclude causation because this study was an experiment AND the results are statistically significant.

Incorrect. Yes, we can conclude causation because this study was an experiment AND the results are statistically significant.

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Correct. The largest contributor to the chi-square test statistic is the top cell on the right. This is the “desipramine/no relapse” cell.

Incorrect. The largest contributor to the chi-square test statistic is the top cell on the right. This is the “desipramine/no relapse” cell.

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Correct. Since desipramine had the lowest relapse rate at 42% whereas lithium and placebo rates were 75% and 83% respectively, we would recommend desipramine as the treatment of choice.

Incorrect. Since desipramine had the lowest relapse rate at 42% whereas lithium and placebo rates were 75% and 83% respectively, we would recommend desipramine as the treatment of choice.

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