# A Hypothesis Is a Claim

**Topics:**Statistics, Arithmetic mean, Statistical hypothesis testing

**Pages:**4 (805 words)

**Published:**December 1, 2012

Population mean

The mean monthly cell phone bill in this city is μ = $42

Population proportion

Example: The proportion of adults in this city with cell phones is π = 0.68 States the claim or assertion to be tested

Is always about a population parameter, not about a sample statistic

Is the opposite of the null hypothesis

e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo

Alternative never contains the “=”sign

May or may not be proven

Is generally the hypothesis that the researcher is trying to prove

Is the opposite of the null hypothesis

e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo

Alternative never contains the “=”sign

May or may not be proven

Is generally the hypothesis that the researcher is trying to prove

Is the opposite of the null hypothesis

e.g., The average diameter of a manufactured bolt is not equal to 30mm ( H1: μ ≠ 30 ) Challenges the status quo

Alternative never contains the “=”sign

May or may not be proven

Is generally the hypothesis that the researcher is trying to prove

If the sample mean is close to the stated population mean, the null hypothesis is not rejected.

If the sample mean is far from the stated population mean, the null hypothesis is rejected.

How far is “far enough” to reject H0?

The critical value of a test statistic creates a “line in the sand” for decision making -- it answers the question of how far is far enough.

Type I Error

Reject a true null hypothesis

Considered a serious type of error

The probability of a Type I Error is

Called level of significance of the test

Set by researcher in advance

Type II Error

Failure to reject a false null hypothesis

The probability of a Type II Error is β

Type I and Type II errors cannot happen at

the same time

A Type I error can only occur if H0 is true

A Type II error can only...

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