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

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.
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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
 ________________________________________________________________________
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3. AP/H Statistics
Guided Notes
Mrs. LeBlanc – Perrone
o Sample Test Statistic

o P-Value
 ________________________________________________________________________
________________________________________________________________________
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4. AP/H Statistics
Guided Notes
Mrs. LeBlanc – Perrone
How to Test Paired Differences Using The Student’s 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. ________________________________________________________________________
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5. AP/H Statistics
Guided Notes
Mrs. LeBlanc – Perrone
Example: Paired Differences
A team of heart surgeons at Saint Ann’s 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.
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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:
__________________________________________________________________________________________
__________________________________________________________________________________________
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