ec41lecture15_handout - Statistics for Economists Lecture...

Unformatted text preview: 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......
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