ec41lecture15_handout - Statistics for Economists Lecture...

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Statistics for Economists
Lecture 15
Kata Bognar
UCLA
May 25, 2010

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Announcements
•
Midterm 2 scores are online.

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Last Lecture
•
t-Interval procedure
•
Hypothesis testing

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Today’s Outline
1
Hypothesis tests for the population mean
2
z-Test, critical and p-value approach
3
t-Test
4
Readings: Weiss, Chapter 9.2 - 9.3, 9.5 - 9.6
5
Readings for next class: Weiss, Chapter 12.1 - 12.2

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Decision Rule in Hypothesis
Testing
•
We decide about the rejection or non-rejection of the null
hypothesis based on the value of a test statistic for the sample.
•
The rejection region is the set of values for the test statistics
that leads to rejection of the null hypothesis.
•
The non-rejection region is the set of values for the test
statistics that leads to non-rejection of the null hypothesis.
•
The critical values of the test statistic separate the rejection
regions from the non-rejection region.
•
The critical value(s) depend on the significance level of the test.

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Decision Rule in Hypothesis
Testing - Example
Transaction times at the ATMs of a particular bank have a
distribution with mean 270 and standard deviation 24 seconds...
•
Assuming that the null hypothesis is true,
¯
X is approximately
normally distributed with μ
¯ x
= 270 and σ = 24 /
√
64 = 3 .
•
Decision rule:
•
reject the null if the sample mean is not higher than 264
= ⇒ rejection region:
¯
X ≤ 264 .
• do not reject the null if the sample mean is higher than 264
= ⇒ non-rejection region:
¯
X > 264 .
• The significance level of this test is about 2 . 5% .

Statistics for
Economists
Lecture 15
Kata Bognar
UCLA
Hypothesis Tests
Hypothesis Test
for the
Population Mean
Decision Rule in Hypothesis
Testing - Example (cont.)
Transaction times at the ATMs of a particular bank have a
distribution with mean 270 and standard deviation 24 seconds...