BUS105_Seminar4_Tutor_Copy(Jess)-e.pptx - BUS105 Statistics...

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BUS105 Statistics Seminar 4
Learning Objectives 1. Execute the Hypothesis Testing (two-samples) for the population mean and proportion population Select and execute an appropriate hypothesis testing for two-sample mean or proportion. Execute a hypothesis to determine whether the variances of two populations are equal. 2. Apply an Analysis of Variance (ANOVA) procedure to compare the means of independent random samples Use hypothesis testing to compare means of independent random samples. 2
Topics Unit 2 1 Point Estimation and Confidence Intervals 2.1 Hypothesis Tests: One-Sample 2.2 Hypothesis Tests: Two-Sample 3 Analysis of Variance (ANOVA) 3
Unit 2 - Chapter 2 Hypothesis tests: Two-Sample Tests
Recap: Hypothesis and Hypothesis Testing HYPOTHESIS A statement about the value of a population parameter developed for the purpose of testing. HYPOTHESIS TESTING A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. 5
Comparing Two Population Means H 0 : µ 1 = µ 2 H 0 : µ 1 ≥ µ 2 µ 1 ≤ µ 2 H 1 : µ 1 ≠ µ 2 H 0 : µ 1 < µ 2 µ 1 > µ 2 where Reject H 0 if p-value < α Equal and Known Variance Equal but Unknown Variance Use t distribution if: One or both of the samples have less than 30 observations, and The population standard deviations are unknown. What are the assumptions that one needs to check before performing the two tests? 6 Test statistics Hypothesis Decision Rule 2 2 2 1 2 1 2 1 n n X X z 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 2 n n s n s n s p 2 1 2 2 1 2 1 1 2 1 n n s X X t p n n
Two-Sample Tests of Proportions We investigate whether two samples came from populations with an equal proportion of successes. The formula for computing the value of z is: 7
Comparing Two Population Proportions H 0 : 1 = 2 H 0 : 1 2 H 0 : 1 2 H 1 : 1 2 H 1 : 1 < 2 H 1 : 1 > 2 8 Test statistics Hypothesis Decision Rule
Dependent vs. Independent Samples How do we tell between dependent and independent samples? 1. A dependent sample is characterized by a measurement followed by an intervention of some kind and then another measurement. This could be called a “before” and “after” study. 2. Dependent sample is characterized by matching or pairing observation. Dependent samples are samples that are paired or related in some fashion.

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