# STA 205 Lecture 11: Packet 11 - Two Sample Inferences

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Clicker question

1variable timewith symptoms

independent samples

NO way to match up

someone who treated a

migraine with medication

or acupuncture

2Compare on an individual

level

Packet 11: Two Sample Inferences for the Mean

After completing this material, you should be able to:

• identify whether two samples are independent or dependent.

• conduct a hypothesis test for the mean difference (µd) when dependent samples are taken.

• calculate a confidence interval estimating the mean difference (µd) when dependent samples are taken.

• conduct a hypothesis test for the difference in the means (µ1 - µ2) when independent samples are taken.

• calculate confidence interval estimating the difference in the means (µ1 - µ2) when independent samples are taken.

To celebrate baseball’s Opening Day … a baseball enthusiast wants to compare the mean batting average for the Cincinnati

Reds & the Philadelphia Phillies.

What variable will be recorded for the sampled players? Is the variable quantitative or categorical?

To make the comparison, he needs to gather 2016 batting averages from members of each team. This can be done using

one of the following two scenarios:

Scenario 1: The individual samples 5 players from the

Reds’ roster and records each player’s batting average.

Then, he samples 5 players from the Phillies’ roster and

records each player’s batting average.

Scenario 2: The individual randomly samples 5

positions in the batting line-up from 9 possible and

records the batting average for the player batting in

that position on each team.

In both sampling scenarios described, the sports enthusiast ends up with 5 batting averages for the Reds and 5 batting

averages for the Phillies. But, the way in which these samples were taken were fundamentally different. One scenario

employed the use of dependent (or paired) samples, while the other used independent samples. Let’s define these two

sampling techniques:

Dependent samples:

Independent samples:

Type of Samples:

Type of Samples:

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