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Page 1: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimation, Hypothesis Testing

and Type II Error

Page 2: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Elementary Statistics with R

Page 3: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimation

Page 4: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimation

Page 5: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimation (2)

Page 6: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Point Estimate of Population Mean

Page 7: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Point Estimate of Population Mean (2)

Page 8: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Known Variance

Page 9: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Known Variance (2)

Page 10: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Known Variance (3)

Page 11: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Known Variance (4)

Page 12: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Known Variance (5)

Page 13: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Unknown Variance

Page 14: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Unknown Variance (2)

Page 15: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Unknown Variance (3)

Page 16: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population Mean

with Unknown Variance (4)

Page 17: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Sampling Size of Population Mean

Page 18: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Sampling Size of Population Mean (2)

Page 19: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Point Estimate of Population

Proportion

Page 20: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Point Estimate of Population

Proportion (2)

Page 21: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population

Proportion

Page 22: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population

Proportion (2)

Page 23: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population

Proportion (3)

Page 24: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Interval Estimate of Population

Proportion (4)

Page 25: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Sampling Size of Population

Proportion

Page 26: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Sampling Size of Population

Proportion (2)

Page 27: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Hypothesis Testing

Page 28: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Hypothesis Testing

Page 29: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Known Variance

Page 30: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Known Variance (2)

Page 31: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Known Variance (3)

Page 32: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Known Variance (4)

Page 33: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Known Variance

Page 34: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Known Variance (2)

Page 35: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Known Variance (3)

Page 36: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Known Variance (4)

Page 37: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Known Variance

Page 38: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Known Variance (2)

Page 39: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Known Variance (3)

Page 40: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Known Variance (4)

Page 41: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Unknown Variance

Page 42: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Unknown Variance (2)

Page 43: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Unknown Variance (3)

Page 44: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population Mean

with Unknown Variance (4)

Page 45: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Unknown Variance

Page 46: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Unknown Variance (2)

Page 47: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Unknown Variance (3)

Page 48: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population Mean

with Unknown Variance (3)

Page 49: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Unknown Variance

Page 50: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Unknown Variance (2)

Page 51: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Unknown Variance (3)

Page 52: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population Mean

with Unknown Variance (4)

Page 53: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population

Proportion

Page 54: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population

Proportion (2)

Page 55: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population

Proportion (3)

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Lower Tail Test of Population

Proportion (4)

Page 57: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population

Proportion (5)

Page 58: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Lower Tail Test of Population

Proportion (5)

Page 59: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population

Proportion

Page 60: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Upper Tail Test of Population

Proportion (2)

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Upper Tail Test of Population

Proportion (3)

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Upper Tail Test of Population

Proportion (4)

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Upper Tail Test of Population

Proportion (5)

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Upper Tail Test of Population

Proportion (5)

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Two-Tailed Test of Population

Proportion

Page 66: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population

Proportion (2)

Page 67: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population

Proportion (3)

Page 68: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Two-Tailed Test of Population

Proportion (4)

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Two-Tailed Test of Population

Proportion (5)

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Type II Error

Page 71: Interval Estimation, Hypothesis Testing and Type II Errorpoincare.matf.bg.ac.rs/~vladaf/Courses/PmfBl H HI... · 2016. 2. 21. · vladaf@matf.bg.ac.rs 31 / 96 Lower Tail Test of Population

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Type II Error

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Type II Error in Lower Tail Test of

Population Mean with Known Variance

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Type II Error in Lower Tail Test of

Population Mean with

Known Variance (2)

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Type II Error in Lower Tail Test of

Population Mean with

Known Variance (3)

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Type II Error in Lower Tail Test of

Population Mean with

Known Variance (4)

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Type II Error in Upper Tail Test of

Population Mean with

Known Variance

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Type II Error in Upper Tail Test of

Population Mean with

Known Variance (2)

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Type II Error in Upper Tail Test of

Population Mean with

Known Variance (3)

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Type II Error in Upper Tail Test of

Population Mean with

Known Variance (4)

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Type II Error in Two-Tailed Test of

Population Mean with

Known Variance

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Type II Error in Two-Tailed Test of

Population Mean with

Known Variance (2)

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Type II Error in Two-Tailed Test of

Population Mean with

Known Variance (3)

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Type II Error in Two-Tailed Test of

Population Mean with

Known Variance (4)

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Type II Error in Lower Tail Test of

Population Mean with

Unknown Variance

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Type II Error in Lower Tail Test of

Population Mean with

Unknown Variance (2)

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Type II Error in Lower Tail Test of

Population Mean with

Unknown Variance (3)

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Type II Error in Lower Tail Test of

Population Mean with

Unknown Variance (4)

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Type II Error in Upper Tail Test of

Population Mean with

Unknown Variance

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Type II Error in Upper Tail Test of

Population Mean with

Unknown Variance (2)

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Type II Error in Upper Tail Test of

Population Mean with

Unknown Variance (3)

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Type II Error in Upper Tail Test of

Population Mean with

Unknown Variance (4)

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Type II Error in Two-Tailed Test of

Population Mean with

Unknown Variance

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Type II Error in Two-Tailed Test of

Population Mean with

Unknown Variance (2)

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Type II Error in Two-Tailed Test of

Population Mean with

Unknown Variance (2)

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Type II Error in Two-Tailed Test of

Population Mean with

Unknown Variance (3)

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Acknowlegments

Some parts of the material in this presentation is

taken from http://www.r-tutor.com/

Deo materijala je preuzet sa sajta

http://www.e-statistika.rs