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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 10

Lesson 8: Confidence intervals for the difference of two proportions

# Examples identifying conditions for inference on two proportions

Examples identifying conditions for confidence intervals and tests about two proportions.

## Want to join the conversation?

• Why don't the two samples have to have the same size?
• I think it has to do with the fact that we are using proportions and not any other statistics. Because if you think about it, 3/4=0.75, but so is 6/8. There are two different samples sizes, but the same proportion of successes.

edit However, if I were you I would just double check with my teacher or consult Google. :)
• in example one it said the following "A sociologist suspects that men are more likely to have received a ticket for speeding than women are. The sociologist wants to sample people and create a two-sample Z interval, in other videos we introduced what that idea is, to estimate the difference between the proportion of men who have received a speeding ticket and the proportion of women who have received a speeding ticket. Which of the following are conditions for this type of interval? Choose all answers that apply." My question is this. Why is A the answer when it says you choose 10 people who have gotten a ticket for speeding and 10 who have not? I feel that this is a little bias to do this because they are divided into groups instead of chosen at random as C says. can someone explain it a little better for me? thanks
• The samples are choose in random, answer A use the word 'include', not 'choose'. what answer A try to say is AFTER sampling, there needs at least 10 for both success and failure case, if it doesn't, we may need to keep doing random sampling until the condition is met.
• A biologist is studying a certain disease affecting oak trees in a forest. They are curious if there's a difference in the proportion of trees that are infected in the North and South sections of the forest. They want to take a sample of trees from each section and do a two-proportion z-test to test their hypotheses.

Which of the following are required for this type of test? Select all that apply.

The trees that are samples are selected randomly.

They observe at least 10 trees with the disease and 10 trees without the disease in each sample.

They sample an equal number of trees from each region of the forest.
(1 vote)
• I'm taking this chapter in school right now, and I am familiar with the Random Condition Normal(Large Counts) Condition, but I have never heard of the Independence Condition. Can someone explain what it is? (@)
(1 vote)