Chapter 9.ppt - Chapter 9 Learning Objectives LO 9.1 LO 9.2...

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9 -1 Hypothesis Testing Chapter 9 Learning Objectives LO 9.1 Define the null hypothesis and the alternative hypothesis. LO 9.2 Distinguish between Type I and Type II errors. LO 9.3 Conduct a hypothesis test using the p -value approach. LO 9.4 Conduct a hypothesis test using the critical value approach. LO 9.5 Differentiate between the test statistics for the population mean. LO 9.6 Specify the test statistic for the population proportion.
9 -2 9.1 Introduction to Hypothesis Testing Hypothesis tests: is the testing of a hypotheses (generally established ideas, beliefs or claims.) In a hypothesis test, define H 0 , the null hypothesis , the default belief or status quo (established hypothesis). H A , the alternative hypothesis , a contradiction of the default believe or status quo. Example: Prior research finds that the average weekly income of graduated workers is $1200. A new researcher claims that it is different. The null and alternative hypotheses are: H 0 : µ= $1200 H A : µ≠$1200
9 -3 Hypothesis Testing Use the following signs in hypothesis tests specify the status quo, contradict H 0 . Note that H 0 always contains the “equality.” H 0 = > < H A < > 9.1 Introduction to Hypothesis Testing On the basis of sample information, we can either Reject the null hypothesis Sample evidence is inconsistent with H 0 . Do not reject the null hypothesis Sample evidence is not inconsistent with H 0 .
9 -4 One tailed test: is when H A includes > or < symbols. Example: If the general belief is that the average life expectancy in most developing countries is less than or equal to 70 years, but a researcher claims that it is more than 70 years, then 9.1 One-Tailed versus Two-Tailed Hypothesis Tests H 0 : <  versus H A : >  ( right-tail test ) On the other hand, if the general belief is that the average life expectancy in most developed countries is greater than or equal to 70, but a researcher claims that it is less than 70 years then H 0 : >  versus H A : <  ( left-tail test ) Note that the inequality in H A determines which tail area will be used to make the decision regarding the rejection of H 0 .
9 -5 9.1 One-Tailed versus Two-Tailed Hypothesis Tests A one-tail hypothesis test is used when the alternative hypothesis is stated as < or > Right tail test : reject the null hypothesis, if the test result is in the yellow area as indicated below, otherwise do not reject. Reject H 0 Reject H 0 Reject H 0 Do not reject H 0 Reject H 0 0 H Do not reject H 0 Left tail test : reject the null hypothesis if the test result is in the yellow area as indicated below, otherwise do not reject.

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