Statistics 101

Chapter 10

Section 2

How to run a significance test

Step 1: Identify the population of interest and the parameter you want to draw conclusions about. State the null and alternative hypothesis in words and symbols.

Step 2: Choose the appropriate inference procedure. Verify the conditions for using the selected process.

Step 3: Carry out the inference procedure. Calculate the test statistic and find the P-value.

Step 4: Interpret your results in the context of the problem.

Tests of significance

Confidence intervals – estimate a population parameter

Tests of significance: assess the evidence provided by data about some claim concerning a population

An outcome that would rarely happen if a claim were true is good evidence that the claim is not true.

Reasoning of tests of significance

Null hypothesis: there is no effect or change in the population H0 (H-nought)

Sweetness of colas: H0:μ = 0

Alternative Hypothesis: Ha is that the cola does lose sweetness.

Ha: μ > 0

P - value

Probability of a result at least as far out as the result we actually got.

Small P-values are evidence against H0 because they say that the observed result is unlikely to occur just by chance.

How small is small enough to persuade us? 0.05 is statistically significant.

Stating Hypotheses

Null hypothesis. Alternative hypothesis

H0: μ = 0

Ha: μ > 0 This is called one-sided because we are

interested only in deviations from the null hypothesis in one direction.

Two-sided

Job Diagnosis Survey p 565 H0: μ = 0

Ha: μ = 0

Statistical Significance

If the P-value is as small or smaller than alpha, we say that the data are statistically significant at level alpha

Test for population mean

Identify the population of interest and the parameter

State the null and alternative hypothesis in words and symbols

Choose the appropriate inference procedure Calculate the test statistic Find the P-value Interpret your results

Z test for a population mean

To test H0: μ = μ0 based on an SRS of size n with unknown μ and known standard deviation σ, compute one-sample z statistic

Z = (x - μ0 ) / σ / √n

Tests with fixed significance level

Fail to reject instead of accept implies a 100% certainty in H0

Since 0.06 > 0.05 we fail to reject the H0. There is not significance to conclude that the students are less skilled.

This is example 10.15

Exercises

10.27, 10.29 – 10.32, 10.33, 10.38, 10.40, 10.41, 10.45, 10.49, 10.56