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StatTutor Lesson - Uses of the Chi-Square Test

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      Questions 1-3

      110

      Question 1.

      How should data be collected for a chi-square test?

      A.
      B.
      C.
      D.

      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.
      2
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      Question 4

      460

      Question 4.

      What method of data collection was used in the following study? “At a large church sponsored university 329 students were surveyed by phone using an SRS and asked their class standing and whether they thought kissing on a first data was appropriate.”

      A.
      B.
      C.

      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.
      2
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      Question 5

      501

      Question 5.

      What method of data collection was used in the following study? “Newly laid Python eggs were randomly assigned to one of three temperatures; at the end of the study eggs were classified as either ‘hatched’ or ‘didn’t hatch’.”

      A.
      B.
      C.

      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.
      2
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      Question 6

      543

      Question 6.

      What method of data collection was used in the following study? “Random samples were taken from three different countries—the United States, India and France. Each respondent was asked whether they think it is wrong to have a baby if ther are not married.”

      A.
      B.
      C.

      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.
      2
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      Question 7

      650

      Question 7.

      In addition to proper data collection, what other condition is required for the P-value from a chi-square test to be trusted?

      A.
      B.
      C.

      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.
      2
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      Question 8

      705

      Question 8.

      How many treatments will be compared in this study?

      A.
      B.
      C.

      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.
      2
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      Question 9

      724

      Question 9.

      True or false: If the response variable had been quantitative rather than categorical, then a chi-square test should not have been used to analyze the data from this study.

      A.
      B.

      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.
      2
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      Question 10

      737

      Question 10.

      What null hypothesis will test the equality of the proportions of relapse for the three treatments?

      A.
      B.
      C.
      D.

      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.
      2

      Question 11

      785

      Question 11.

      Why were the patients randomly allocated to the treatments?

      A.
      B.
      C.

      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.
      2

      Question 12

      803

      Question 12.

      Assuming that the null hypothesis is true, how many patients do we expect to relapse taking lithium?

      A.
      B.
      C.
      D.

      Correct. expected = (rowtotal)(columntotal)tabletotal = (14)(24)72 = 16
      Incorrect. expected = (rowtotal)(columntotal)tabletotal = (14)(24)72 = 16
      2

      Question 13

      891

      Question 13.

      Are the expected counts large enough so that the chi-square test statistic has an approximate chi-square distribution?

      A.
      B.

      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.
      2

      Question 14

      978

      Question 14.

      What is the contribution to the chi-square test statistic for the placebo/relapse cell?

      A.
      B.
      C.
      D.
      E.
      F.

      Correct. The contribution to the chi-square test statistic for the placebo/relapse cell is (observedexpected)2expected=(2016)216=1.00
      Incorrect. The contribution to the chi-square test statistic for the placebo/relapse cell is (observedexpected)2expected=(2016)216=1.00
      2

      Question 15

      1000

      Question 15.

      What are the degrees of freedom for this chi-square test?

      A.
      B.
      C.
      D.
      E.

      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
      2

      Question 16

      1036

      Question 16.

      With P-value = 0.0052 and α = 0.02, can we reject the null hypothesis?

      A.
      B.

      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.
      2

      Question 17

      1053

      Question 17.

      For this study, can we conclude that the type of treatment causes a difference in the relapse rates?

      A.
      B.

      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.
      2

      Question 18

      1136

      Question 18.

      Which cell is the largest contributor to the chi-square test statistic?

      A.
      B.
      C.
      D.
      E.
      F.

      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.
      2

      Question 19

      1177

      Question 19.

      What treatment would you recommend for a patient who wants to break their cocaine habit?

      A.
      B.
      C.

      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.
      2