Sta 291 fall 2009
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STA 291 Fall 2009. Lecture 21 Dustin Lueker. Example. If the null hypothesis is rejected at a 2% level of significance, will the null be rejected at a 5% level of significance? Yes No Maybe. Example.

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STA 291 Fall 2009

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Sta 291 fall 2009

STA 291Fall 2009

Lecture 21

Dustin Lueker


Example

Example

  • If the null hypothesis is rejected at a 2% level of significance, will the null be rejected at a 5% level of significance?

    • Yes

    • No

    • Maybe

STA 291 Fall 2009 Lecture 21


Example1

Example

  • If the null hypothesis is rejected at a 2% level of significance, will the null be rejected at a 1% level of significance?

    • Yes

    • No

    • Maybe

STA 291 Fall 2009 Lecture 21


Test statistic

Test Statistic

  • Testing µ

    • Without the aide of some type of technology it is impossible to find exact p-values when using this test statistic, because it is from the t-distribution

STA 291 Fall 2009 Lecture 21


Testing the difference between means from different populations

Testing the Difference Between Means from Different Populations

  • Hypothesis involves 2 parameters from 2 populations

    • Test statistic is different

      • Involves 2 large samples (both samples at least 30)

        • One from each population

  • H0: μ1-μ2=0

    • Same as H0: μ1=μ2

    • Test statistic

STA 291 Fall 2009 Lecture 21


Example2

Example

  • In the 1982 General Social Survey, 350 subjects reported the time spend every day watching television. The sample yielded a mean of 4.1 and a standard deviation of 3.3.

  • In the 1994 survey, 1965 subjects yielded a sample mean of 2.8 hours with a standard deviation of 2.

    • Set up hypotheses of a significance test to analyze whether the population means differ in 1982 and 1994 and test at α=.05 using the p-value method.

STA 291 Fall 2009 Lecture 21


Small sample tests for two means

Small Sample Tests for Two Means

  • Used when comparing means of two samples where at least one of them is less than 30

    • Normal population distribution is assumed for both samples

  • Equal Variances

    • Both groups have the same variability

  • Unequal Variances

    • Both groups may not have the same variability

STA 291 Fall 2009 Lecture 21


Small sample test for two means equal variances

Small Sample Test for Two Means, Equal Variances

  • Test Statistic

    • Degrees of freedom

      • n1+n2-2

STA 291 Fall 2009 Lecture 21


Small sample confidence interval for two means equal variances

Small Sample Confidence Interval for Two Means, Equal Variances

  • Degrees of freedom

    • n1+n2-2

STA 291 Fall 2009 Lecture 21


Small sample test for two means unequal variances

Small Sample Test for Two Means, Unequal Variances

  • Test statistic

  • Degrees of freedom

STA 291 Fall 2009 Lecture 21


Small sample confidence interval for two means unequal variances

Small Sample Confidence Interval for Two Means, Unequal Variances

STA 291 Fall 2009 Lecture 21


Method 1 equal variances vs method 2 unequal variances

Method 1 (Equal Variances) vs. Method 2 (Unequal Variances)

  • How to choose between Method 1 and Method 2?

    • Method 2 is always safer to use

    • Definitely use Method 2

      • If one standard deviation is at least twice the other

      • If the standard deviation is larger for the sample with the smaller sample size

    • Usually, both methods yield similar conclusions

STA 291 Fall 2009 Lecture 21


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