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1. Paired data involves dependent samples that are measured in pairs, such as measurements taken from the same subject before and after a treatment. When comparing paired data, the proper test is a one-sample t-test on the differences between pairs. 2. The null hypothesis for a paired t-test states that the mean of the differences between pairs is equal to zero, indicating no change between measurements. The alternative hypothesis depends on the specific problem but can be left-tailed, right-tailed, or two-tailed. 3. The key steps in a paired t-test are calculating the differences between pairs, finding the mean and standard deviation of the differences, determining the t-statistic, computing the

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AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Name: ______________________________ Date: ___________ 8.4 Tests Involving Paired Differences (Dependent Samples) Paired Data o Many statistical applications use _______________________samples to draw conclusions about the _____________________________________________________________________. Examples: Before and after situations ________________________________________ ________________________________________ o When a test involves comparing two populations for which the data occur in pairs, the proper procedure is to run a one-sample test on a single variable consisting of the differences from the paired data. 1
AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Components of the Paired Test o Hypotheses When testing the mean of the differences of paired data values, the null hypothesis states that _____________________________________________________ ( ) The null hypothesis is always ___________________ The alternate hypothesis depends on the problem and can be: Left-Tailed Right-Tailed Two-Tailed o ________________________________________________________________________ Take the measurements from one set measurements of the other set, then find the mean (add up the differences and divide by the number of data pairs) This can be done in the calculator o Enter the after values in L1 o Enter the before values in L2 o Highlight L3, type L1 L2, press ENTER (L3 should populate with the differences) o Hit Stat, tab over to calc, choose 1:1-Var Stats, use L3 hit ENTER S o For paired difference tests, we make our decision regarding H0 according to the evidence of _______ o ________________________________________________________________________ 2
AP/H Statistics Guided Notes Mrs. LeBlanc Perrone o Sample Test Statistic o P-Value ________________________________________________________________________ ________________________________________________________________________ 3
AP/H Statistics Guided Notes Mrs. LeBlanc Perrone How to Test Paired Differences Using The Students Distribution 1. ________________________________________________________________________ Do you have a random sample of matched data pairs? Identify , and Is the distribution normal, mound-shaped symmetrical, or is ? 2. State the null and alternate hypotheses, Identify the level of significance 3. ________________________________________________________________________ Sample Test Statistic: 4. ________________________________________________________________________ Use a T-test 5. ________________________________________________________________________ If P-value , we reject If P-value > , we fail to reject 6. ________________________________________________________________________ 4
AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Example: Paired Differences A team of heart surgeons at Saint Anns Hospital knows that many patients who undergo corrective heart surgery have a dangerous buildup of anxiety before their scheduled operations. The staff psychiatrist at the hospital has started a new counseling program intended to reduce this anxiety. A test of anxiety is given to patients who know they must undergo heart surgery. Then each patient participates in a series of counseling sessions with the staff psychiatrist. At the end of the counseling sessions, each patient is retested todetermine anxiety level. Table 8-8 indicates the results for a random sample of nine patients. Higher scores mean higher levels of anxiety. Assume the distribution of differences is mound-shaped and symmetric. From the given data, can we conclude that the counseling sessions reduce anxiety? Use a 0.01 level of significance. 5
AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Summary Questions 1. Are data that can be paired independent or dependent? (Hint: we talked about independent and dependent in Chapter 7) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. When testing the difference of means for paired data, what is the null hypothesis? What does it mean? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. What elements of testing with P-values are consistent in every situation ( )? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 6

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8.4 guided notes

  • 1. AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Name: ______________________________ Date: ___________ 8.4 Tests Involving Paired Differences (Dependent Samples) Paired Data o Many statistical applications use _______________________samples to draw conclusions about the _____________________________________________________________________. Examples: Before and after situations ________________________________________ ________________________________________ o When a test involves comparing two populations for which the data occur in pairs, the proper procedure is to run a one-sample test on a single variable consisting of the differences from the paired data. 1
  • 2. AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Components of the Paired Test o Hypotheses When testing the mean of the differences of paired data values, the null hypothesis states that _____________________________________________________ ( ) The null hypothesis is always ___________________ The alternate hypothesis depends on the problem and can be: Left-Tailed Right-Tailed Two-Tailed o ________________________________________________________________________ Take the measurements from one set measurements of the other set, then find the mean (add up the differences and divide by the number of data pairs) This can be done in the calculator o Enter the after values in L1 o Enter the before values in L2 o Highlight L3, type L1 L2, press ENTER (L3 should populate with the differences) o Hit Stat, tab over to calc, choose 1:1-Var Stats, use L3 hit ENTER S o For paired difference tests, we make our decision regarding H0 according to the evidence of _______ o ________________________________________________________________________ 2
  • 3. AP/H Statistics Guided Notes Mrs. LeBlanc Perrone o Sample Test Statistic o P-Value ________________________________________________________________________ ________________________________________________________________________ 3
  • 4. AP/H Statistics Guided Notes Mrs. LeBlanc Perrone How to Test Paired Differences Using The Students Distribution 1. ________________________________________________________________________ Do you have a random sample of matched data pairs? Identify , and Is the distribution normal, mound-shaped symmetrical, or is ? 2. State the null and alternate hypotheses, Identify the level of significance 3. ________________________________________________________________________ Sample Test Statistic: 4. ________________________________________________________________________ Use a T-test 5. ________________________________________________________________________ If P-value , we reject If P-value > , we fail to reject 6. ________________________________________________________________________ 4
  • 5. AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Example: Paired Differences A team of heart surgeons at Saint Anns Hospital knows that many patients who undergo corrective heart surgery have a dangerous buildup of anxiety before their scheduled operations. The staff psychiatrist at the hospital has started a new counseling program intended to reduce this anxiety. A test of anxiety is given to patients who know they must undergo heart surgery. Then each patient participates in a series of counseling sessions with the staff psychiatrist. At the end of the counseling sessions, each patient is retested todetermine anxiety level. Table 8-8 indicates the results for a random sample of nine patients. Higher scores mean higher levels of anxiety. Assume the distribution of differences is mound-shaped and symmetric. From the given data, can we conclude that the counseling sessions reduce anxiety? Use a 0.01 level of significance. 5
  • 6. AP/H Statistics Guided Notes Mrs. LeBlanc Perrone Summary Questions 1. Are data that can be paired independent or dependent? (Hint: we talked about independent and dependent in Chapter 7) ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 2. When testing the difference of means for paired data, what is the null hypothesis? What does it mean? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 3. What elements of testing with P-values are consistent in every situation ( )? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ HOT Question: __________________________________________________________________________________________ __________________________________________________________________________________________ 6