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Hypothesis Testing for a Mean

Hypothesis Testing for a Mean

Author: mary daunis

-illustrate a hypthesis test for a mean when the population standard deviation is not known

-explore the difference between claims stated with < symbol and with ≤ symbol

Properly identifying the stated claim in a hypothesis testing process is key to succesfully composing the correct final conclusion. In this packet, I use slightly different wording for the claim in two hypothesis tests and show othe effect on the wording of the conclusion.

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Hypothesis Test for a Mean - Claim has ≤

In this statement of the problem, the population standard deviation is not known and the claim is stated using a ≤ symbol. Pay close attention to how the alternative hypothesis is formed - a common point of confusion is that the alternative hypothesis is always the opposite of the claim but this is not the case. Rather, the alternative hypothesis is either the same as the claim or the opposite of the claim - it depends on how the claim is stated.

Hypothesis Test for a Mean - Claim has <

Here I show how a small change in the wording of the original claim makes a big difference in the form of the alternative hypothesis, which in turn alters the wording of the final conclusion.