ap stats study guides

โœŒ๏ธย  Unit 2 - Exploring Two-Variable Data

โš–๏ธย  Unit 6 - Inference for Categorical Data: Proportions

๐Ÿ˜ผย  Unit 7 - Inference for Qualitative Data: Means

โœณ๏ธย  Unit 8 Inference for Categorical Data: Chi-Square

๐Ÿ“ˆย  Unit 9 - Inference for Quantitative Data: Slopes

๐Ÿงย  Multiple Choice Questions (MCQs)

7.7 Justifying a Claim About the Difference of Two Means Based on a Confidence Interval

#confidenceintervals

#differenceoftwomeans

โฑ๏ธย ย 2 min read

written by

Josh Argo

josh argo


Testing A Claim

As you recall from Unit 7.3, a statistical claim is any belief that any population is equal (or not equal) to a given number or proportion. In dealing with two populations, our statistical claim is generally regarding whether these two populations are the same or different. Our null statistical claim when dealing with two different populations is that they are not different. In other words, their means are the same.

Making A Conclusion

When given a confidence interval and making a conclusion, there is a preset template that we can use that helps us to be sure to include all of the vocabulary necessary to score well on the AP Statistics exam.

Template

Our template should go as follows:

"We are ___% confident that the true difference in population means between _______ and _______ (context of problem) is (___, ___).

As with any AP Statistics Free Response question, it is always imperative that your answer includes context of the problem given.

When testing for the difference in two populations, it is also important to use that interval to test the claim that the two populations are the same. If the two populations are statistically "the same", 0 will be included in your interval. If after completing your interval, you do NOT have 0 in your interval, there is reason to believe that your two populations do, in fact, have different means.

Finishing Our ๐Ÿ to ๐ŸŽ Example

Let's finish our example with the green apples and red apples.

In Unit 7.5, we concluded that our confidence interval for the difference in our two color apples was (0.408, 0.592). Our conclusion should go as follows:

"We are 95% confident that the true difference in the population means of the weights of green apples and red apples is between (0.408, 0.592). Since 0 is not included in our interval, we have significant evidence that the weights of green apples and red apples are in fact different."

Notice since 0 was NOT in our interval, that tells us, with 95% confidence, that there is some sort of difference in our two population means.

https://cdn.pixabay.com/photo/2016/04/02/09/43/apple-1302430_960_720.jpg

image courtesy of pixabay

๐ŸŽฅWatch: AP Stats - Inference: Confidence Intervals for Means

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