Transcript Statistics 101

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