StatTutor Lesson - The Chi-Square Test Statistic

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      Question 1

      73

      Question 1.

      True or false: When computing the chi-square test statistic, a term is computed for each cell and all cell contributions are added together.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
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      Question 2

      122

      Question 2.

      What can we say about the value of the chi-square test statistic?

      A.
      B.
      C.

      Correct. Since the numerator is squared and the denominator is always positive, the chi-square test statistic value is always positive.
      Incorrect. Since the numerator is squared and the denominator is always positive, the chi-square test statistic value is always positive.
      2
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      Questions 3-4

      194

      Question 3.

      Fill in the blank: The closer the observed counts are to their respective expected counts, the ________ the chi-square test statistic is.

      A.
      B.

      Correct. When the observed count equals its respective expected count, the chi-square test statistic is zero and the closer they are, the smaller the test statistic is.
      Incorrect. When the observed count equals its respective expected count, the chi-square test statistic is zero and the closer they are, the smaller the test statistic is.
      2
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      Question 5

      246

      Question 5.

      What distribution do we use to obtain a P-value for a chi-square test statistic?

      A.
      B.
      C.

      Correct. We use a chi-square distribution to find a P-value for a chi-square test statistic.
      Incorrect. We use a chi-square distribution to find a P-value for a chi-square test statistic.
      2
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      Question 6

      358

      Question 6.

      According to this outline, what are the degrees of freedom for a chi-square test statistic?

      A.
      B.
      C.
      D.

      Correct. The degrees of freedom for the chi-square test statistic are (r – 1)(c – 1).
      Incorrect. The degrees of freedom for the chi-square test statistic are (r – 1)(c – 1).
      2
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      Question 7

      396

      Question 7.

      What is the appropriate null hypothesis for this study?

      A.
      B.

      Correct. The appropriate null hypothesis says: There is NO association between student smoking and parent’s smoking.
      Incorrect. The appropriate null hypothesis says: There is NO association between student smoking and parent’s smoking.
      2
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      Question 8

      438

      Question 8.

      What is the name for the red values given in the two-way table?

      A.
      B.

      Correct. The values given in the table are the counts observed in the data.
      Incorrect. The values given in the table are the counts observed in the data.
      2
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      Question 9

      448

      Question 9.

      What do we assume when we compute expected counts?

      A.
      B.
      C.

      Correct. We assume the null hypothesis of no relationship to be true and use the marginals to find the expected counts.
      Incorrect. We assume the null hypothesis of no relationship to be true and use the marginals to find the expected counts.
      2

      Question 10

      489

      Question 10.

      According to the expected counts given in blue in the two-way table, are they big enough for the test statistic to have an approximate chi-square distribution?

      A.
      B.

      Correct. All expected counts are bigger than 5 so the chi-square test statistic will have an approximate chi-square distribution.
      Incorrect. All expected counts are bigger than 5 so the chi-square test statistic will have an approximate chi-square distribution.
      2

      Question 11

      568

      Question 11.

      True or false: There are six terms in this chi-square test statistic because there are six cells in the two-way table.

      A.
      B.

      Correct. We have a term in the chi-square test statistic for every cell in the table.
      Incorrect. We have a term in the chi-square test statistic for every cell in the table.
      2

      Questions 12-13

      624

      Question 12.

      In the degrees of freedom formula (r – 1)(c – 1), what does “r” represent?

      A.
      B.
      C.

      Correct. “r” is the letter “r” for a reason; it represents the number of rows in the table.
      Incorrect. “r” is the letter “r” for a reason; it represents the number of rows in the table.
      2

      Question 14

      670

      Question 14.

      Why did we conclude that there is a relationship?

      A.
      B.

      Correct. When we reject H0, we conclude that Ha is correct. In this situation, we conclude that there is a relationship.
      Incorrect. When we reject H0, we conclude that Ha is correct. In this situation, we conclude that there is a relationship.
      2

      Question 15

      736

      Question 15.

      Which cell correspond to the value of 16.83 in the test statistic?

      A.
      B.
      C.
      D.

      Correct. The value of 16.83 is in the same position in the computation as the cell “neither parent smokes/student smokes” lies in the two-way table.
      Incorrect. The value of 16.83 is in the same position in the computation as the cell “neither parent smokes/student smokes” lies in the two-way table.
      2

      Question 16

      796

      Question 16.

      Since 22.5% is greater than 13.9%, can we conclude that more students smoke when both parents smoke than when neither parent smokes?

      A.
      B.

      Correct. Yes, we can conclude that the smoking rate of students is higher when both parents smoke than when neither parent smokes.
      Incorrect. Yes, we can conclude that the smoking rate of students is higher when both parents smoke than when neither parent smokes.
      2