9-4: Inferences from Two Dependent Populations

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9-4: Inferences from Two Dependent Populations. College Prep Stats. Dependent Populations. Specific situation in which each data value from one population is paired with another data value from the other population Guarantees that the two populations are the same size

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### 9-4: Inferences from TwoDependent Populations

College Prep Stats

Dependent Populations
• Specific situation in which each data value from one population is paired with another data value from the other population
• Guarantees that the two populations are the same size
• Considers the difference of the pairs to create a special new “difference population”
• Instead of looking at each population separately
Method

The average difference between pairs (parameter)

• Hypothesis test
• Null Hypothesis:
• Alternative Hypothesis
• Remaining steps are the same as any hypothesis test (calc test stat, find p-val, reject/fail to reject, conclude)

0 unless given a specific difference to consider

Test Statistic

The average difference between pairs (statistic)

Test Statistic (Tells you distribution for p-value)

The average difference between pairs (parameter)

Comes from hypotheses

Sample standard deviation of the differences from sample

The size of the two samples (remember they are each the same size)

How to find parts of test statistic
• For each pair of data values, subtract (pop. 1 value – pop. 2 value) = new data value
• All of the new data values will form your “difference population” – enter into calc.
• : sample mean from diff. pop. (given as
• : sample std. dev. from diff. pop. (given as s)
• n: size of the populations (not combined)
Example 1
• A sample of Freshman at Rutgers University were weighed in both August and May to determine if the “freshmen 15” is true. The data values are paired with August weight andMay weight. Test the claim(at .05 significance) that the amount of weight gained is equal to 15 pounds (6.8 kg)
Example 2
• Are best actresses younger than best actors?
• At the .05 significance level, test the claim that best actresses are younger than best actors. The age at the time of winning the award is given paired with the other winner from the same year.
Data for Example 2
• Actress: 28, 32, 27, 27, 26, 24, 25, 29, 41, 40, 27, 42, 33, 21, 35
• Actor: 62, 41, 52, 41, 34, 40, 56, 41, 39, 49, 48, 56, 42, 62, 29
Example 3

Is there more tobacco use than alcohol use in Disney movies?

• Below is paired data the amount of seconds in which tobacco or alcohol is used in selected Disney films (from the same movie). At .05 significance, test the claim that there is more tobacco use than alcohol use
Homework
• P.495: #14, 15, 18a