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 291Fall 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

STA 291 Fall 2009 Lecture 21


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

  • 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

  • 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


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

  • 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

  • Test Statistic

    • Degrees of freedom

      • n1+n2-2

STA 291 Fall 2009 Lecture 21


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

  • Test statistic

  • Degrees of freedom

STA 291 Fall 2009 Lecture 21


Small Sample Confidence Interval for Two Means, Unequal Variances

STA 291 Fall 2009 Lecture 21


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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