# Fundamentals of hypothesis testing: one-sample tests Flashcards

Hypothesis

A hypothesis is a statement (assumption) about a population parameter

Population mean example

Example: The mean monthly mobile phone bill of this city is μ = $72

Population proportion example

Example: The proportion of adults in this city with mobile phones is ∏ = 0.89

The Null Hypothesis, H0

States the belief or assumption in the current situation (status quo)

Begin with the assumption that the null hypothesis is true

(similar to the notion of innocent until proven guilty)

Refers to the status quo

Always contains ‘=‘, ‘≤’ or ‘’ sign

May or may not be rejected

Is always about a population parameter; e.g. μ, not about a sample statistic

The Alternative Hypothesis, H1

Is the opposite of the null hypothesis

e.g. The average number of TV sets in Australia

homes is not equal to 3 ( H1: μ ≠ 3 )

Challenges the status quo

Can only can contain either the ‘’ or ‘≠’ sign

May or may not be proven

Is generally the claim or hypothesis that the researcher is trying to prove

Hypothesis testing process

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The Level of Significance, alpha

hypothesis is true

Defines rejection region of the sampling distribution

Is designated by alpha, (level of significance)

Typical values are 0.01, 0.05, or 0.10

Note relationship to 99%, 95% and 90% confidence levels

Is selected by the researcher at the beginning

Provides the critical value(s) of the test

Level of Significance and the Rejection Region

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Errors in making decisions

Type I error

Reject a true null hypothesis

Considered a serious type of error

Type II error

Fail to reject a false null hypothesis

The probability of errors

The probability of Type I error is alpha

Called level of significance of the test; i.e. 0.01, 0.05, 0.10

Set by the researcher in advance

The probability of Type II error is β

Outcomes and probabilities of hypothesis testing

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Z Test of Hypothesis for the Mean (σ Known)

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Critical Value Approach to Testing

For a two-tail test for the mean, σ known:

Convert sample statistic ( ) to the test statistic (Z statistic)

Determine the critical Z values for a specified level of significance from a Table E.2 or computer

Decision Rule: If the test statistic falls in the rejection region, reject H0 ; otherwise do not reject H0

Two tail tests

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6 STEPS IN HYPOTHESIS TESTING

State the null hypothesis, H0 and the alternative hypothesis, H1

Choose the level of significance, alpha, and the sample size, n

Determine the appropriate test statistic and sampling distribution

Determine the critical values that divide the rejection and non-rejection regions

Collect data and calculate the value of the test statistic

Make the statistical decision and state the managerial conclusion