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How to Set Up a Hypothesis Test: Null versus Alternative

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H0 if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

We are now ready to accept or reject the null hypothesis. If the tcalc > ttab, we reject the null hypothesis. In our case, tcalc=5.88 > ttab=2.45, so we reject the null hypothesis, and say that our sample mean is indeed larger than the accepted limit, and not due to random chance, so we can say that the soil is indeed contaminated.

The null hypothesis is only rejected when we have evidence beyond a reasonable doubt that a

When you about a , you can use your test statistic to decide whether to reject the null hypothesis, H0. You make this decision by coming up with a number, called a -value.

Power = the probability of correctly rejecting a false null hypothesis = 1 - .


In testing a null vs an alternative, if we don't reject the null (e.g

If you only want to see whether the time turns out to be greater than what the company claims (that is, whether the company is falsely advertising its quick prep time), you use the greater-than alternative, and your two hypotheses are

self study - Reject null hypothesis or not? - Cross Validated

Which alternative hypothesis you choose in setting up your hypothesis test depends on what you’re interested in concluding, should you have enough evidence to refute the null hypothesis (the claim). The alternative hypothesis should be decided upon before collecting or looking at any data, so as not to influence the results.

Example Of Not Rejecting The Null Hypothesis

A statistical hypothesis test is a procedure for deciding between two possible statements about a population. The phrase significance test means the same thing as the phrase "hypothesis test."

Hypothesis | Hypothesis | Null Hypothesis

Before actually conducting a hypothesis test, you have to put two possible hypotheses on the table — the null hypothesis is one of them. But, if the null hypothesis is rejected (that is, there was sufficient evidence against it), what’s your alternative going to be? Actually, three possibilities exist for the second (or alternative) hypothesis, denoted Ha. Here they are, along with their shorthand notations in the context of the pie example:

is always given in terms of the null hypothesis

If the results are likely to have occurred under the claim, then you fail to reject H0 (like a jury decides not guilty). If the results are unlikely to have occurred under the claim, then you reject H0 (like a jury decides guilty).