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AP®︎/College Statistics

Course: AP®︎/College Statistics>Unit 10

Lesson 4: Setting up a test for a population proportion

Constructing hypotheses for a significance test about a proportion

Constructing hypotheses for a significance test about a proportion.

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• why is Ha in the second example p >0.9 instead of p not equal to 0.9?
• Because the problem statement indicates the researchers want to test if the proportion is now higher, hence the ">" sign. If it stated "test if the proportion is different" then you'd have an alternative hypothesis of p =\= 0.9
• In the second example, H_a is the hypothesis that p > 0.9 (internet access has increased significantly), while H_0 is the hypothesis that p = 0.9 (internet access is the same as before). Why isn't the null hypothesis that p <= 0.9 (internet access has not increased significantly)?

In other words, the alternative hypothesis is only capturing the "internet access has increased" tail of the normal distribution. There's a nonzero probability that internet access has decreased in a statistically-significant manner, but that probability isn't captured in either H_0 or H_a. Shouldn't that be taken into account?
• Our null hypothesis is based on a certain poll which states that "...about 90% of homes in California had access to the internet". 90%, not 90% or fewer. Thus, null hypothesis is p = 0.9, not p <= 0.9.

Our alternative hypothesis is based on a theory that internet access has become more available. Quote: "...want to test if that proportion is now higher". Meaning, alternative hypothesis is p > 0.9, not p ≠ 0.9.

We do not know why the researchers had that theory, our hypothesis testing is simply based on the data presented.