Chapter 24: Comparing Means (when groups are independent) AP Statistics.
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Transcript of Chapter 24: Comparing Means (when groups are independent) AP Statistics.
![Page 1: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/1.jpg)
Chapter 24: Comparing Means (when groups are independent)
AP Statistics
![Page 2: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/2.jpg)
Sampling Distribution for the Difference of Two Means (when groups are independent)
![Page 3: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/3.jpg)
Sampling Distribution for the Difference of Two Means (when groups are independent)
Formula for degrees of freedom when comparing means of independent groups
The calculator will compute this for you
![Page 4: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/4.jpg)
Assumptions and Conditions
Independence Assumption:Randomization Condition10% Condition
Normal Population Assumption:Need to check each group for normality. SHOW GRAPH.
Nearly Normal Condition
Independent Groups AssumptionJust check for reasonability (this is very important)
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Two-Sample t-interval
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Two-Sample t-test
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Example
Below are the saturated fat content (in grams) for several pizzas sold by two national chains. Create a 95% confidence interval for the difference in the means for the saturated fat content of the two brands.
Brand D 17 12 1 0 8 8 10 10 5 16 16 8 12 15 7 11 11 13 13 11 12
Brand PJ 6 7 11 9 4 4 7 9 11 3 4 5 8 5 5
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Example
In order to create a two-sample t-test, I first need to satisfy the Independent Sample Assumption, the Normal Population Assumption and the Independent Group Assumption. To satisfy these, I will need to satisfy the following conditions
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Example
To satisfy the Independent Samples Assumption, we need to satisfy the below:Randomization Condition: We can assume that the pizzas from each company were picked at random
10% Condition: We assume that the 20 and 15 pizzas are both less than 10% of the pizzas made by each company
![Page 10: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/10.jpg)
Example
To satisfy the Normal Population Condition, I can satisfy the Nearly Normal Condition (remember how sample size plays a role in what we look for)
Brand D Brand PJ
Both distributions of saturated fatroughly unimodal and symmetric.
![Page 11: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/11.jpg)
Example
To satisfy the Independent Groups Assumption, I can assume that the groups are independent. There is no reason to think that the fat content in Brand D is not independent from the fat content in Brand PJ.
Since all the Assumptions and Conditions have been met, we can use a t-distribution with 32.757 degrees of freedom and create a two-sample t-interval.
![Page 12: Chapter 24: Comparing Means (when groups are independent) AP Statistics.](https://reader033.fdocuments.us/reader033/viewer/2022061500/56649f505503460f94c724eb/html5/thumbnails/12.jpg)
Example
757.32 72.4
588.2 53.6 15
193.3 25.11 20
dfyy
syn
syn
DD
PJDPJ
DDD
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Example
978.015
588.2
20
3.193
22
22
PJ
PJ
D
DPJD n
s
n
syySE
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Example
71.6,73.2
99.172.4
978.003.272.4
*8.32
PJDPJD yySEtyy
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Example
We are 95% confident that the true mean fat content of Brand D is between 2.73 and 6.71 grams higher than the true mean fat content for Brand PJ.
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Example
Do the pizza chains have significantly different mean saturated fat contents? Conduct a hypothesis test.
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