Unit 6, Inference for Categorical Data Proportions

Confidence Interval and Level

Confidence Interval

Interpretation: We are---% confident that interval from_to __ captures the true

statistics±(critical value)(standard error of statistics)

Confidence Level

Interpretation: If we take many samples of the same size from this population, about ---% of them will result in an interval that captures the true parameter

Constructing Confidence Interval

C.I. for Population Proportion

Formula for one sample-z interval for proportions

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Conditions(Plan)

  • Random: SRS of ....
  • Independence: Assume at least (n*10)
  • Normality: np̂≥10 and n(1-p̂)≥10

Conclude
Use the Confidence Interval Interpretation

Formula for finding the sample size from given Marginal Error

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Types of Error

Type I Error

Type II Error

image

P(Type I error)=α(significance Level)

P(Type II error)=1-power

Type I error is made when the null hypothesis is actually true but the alternative hypothesis is chosen

  • Reject Ho when it is true

Type II error is made when failing to reject the null hypothesis when it is false

  • Fail to reject Ho when it is false

Significance Test

Hypthoesis

Null Hypothesis(Ho)

Alternative Hypothesis(Ha)

"No difference" statement.
Null means NOT

Ho: P=

Claim we are find evidence for

Ha: P >, <, ≠

P<α

  • Reject the null, there is convincing evidence for Ha(alternative)

P>α

  • Fail to reject the null, there is no convincing evidence for Ha(alternative)

P-Value Interpretation

  • If the [null hypothesis is true], the probability of getting [sample size] is [p-value]

Constructing significance test for population proportions

  • State:
    -Null Hypothesis
    -Alternative Hypothesis
    -Define Parameter
    -Significance Level
  • Plan:
    -Random
    -Independence
    -Normality:np̂≥10 and n(1-p̂)≥10
  • Do:
    -1-sample z-test
    -Normalcdf()
  • Conclude:
    -Reject/Fail to reject the null(Ho), Convincing evidence/No Convincing evidence for alternative(Ha)

1-sample z-test formula Untitled 9

Constructing significance test for difference in two population proportions

  • State:
    -Ho: p1-p2=0
    -Ha: p1-p2 >, < 0
  • Plan
    -Random
    -Independence
    -Normality:n1pc≥10 and n1(1-pc)≥10, n2pc≥10 and n2(1-pc)≥10
  • Do
    -2 Prop Z-Test
  • Conclude
    -Reject/Fail to reject the null(Ho), Convincing evidence/No Convincing evidence for alternative(Ha)

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CI for the Diff. of Two Proportions
Conditions(Plan)

  • Random: SRS of ....
  • Independence: Assume at least (n*10)
  • Normality: n1p̂1≥10 and n1(1-p̂1)≥10, n2p̂2≥10 and n2(1-p̂2)≥10

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Do

  • Use 2-Prop Z-Interval