Ch. 6 Probability

–When there is variability, there is also ‘uncertainty’.

확률은 추론 통계학의 중요한 역할을 한다.

#추론 통계학과 확률이 차이는 무엇인가?

추론 통계학=샘플->모집단

확률=모집단->샘플

 

Random Sampling
•Two Requirements(확률의 정확성)

1.Each individual in the population must have an equal chance of being selected(각각의 개체가 선택될 확률이 같을 것)

2.If more than one individual is to be selected for the sample, there must be constant probability for each and every selection

잘못된 예)

(52장의 카드 중 조커가 나올 확률은? ) = 1/52  그 다음번에 뽑을 때의 확률은? 1/51

=> 동일한 범위가 아니므로 random sampling을 위해서는 경우의 수를 동일할 것.

 

 

–nonrandom sample: convenient sample

–Difficult to determine if it is representative of the population

 

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•Probability and proportion measure the same thing

–N=10 (1,1,2,3,3,4,4,4,5,6), p(X>4)=?

–

–Probability: proportion of area in the frequency distribution graph.

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•Normal distribution 

- Symmetrical. The mean, median, and mode are equal

- 50% of the scores are below the mean, and 50% above it.

- Most of the scores pile up around the mean and extreme scores (high or low) are relatively rare (low frequency)

 

•Exercise

–Mean: 68 inches, s.d.: 6 inches

–Probability of randomly selecting an individual from this population who is taller than 80 inches.

–P(X>80) = ?

–Answer

 

Unit Normal Table

–Lists proportions of the normal distribution corresponding to each z-score value

•Figure 6.6 on p.138 (Complete table: Appendix B on p.A-24)

–Try to Answer

• p (z< -0.50)

–A: 30.85%

•p (-0.40 < z < 1.25)

–A: 54.98%

•SAT distribution (μ=500 and σ=100), p (X > 650)

–A: 6.68%

•p (600 < X < 700)

–A: 13.59%

•Score to be in the top 15% of the SAT score

–A: 604

 

 

•Choice of z=+/- 2.00: arbitrary

–Boundaries separating the middle 95% of the distribution from the extreme 5% in the tail.

–Boundaries are located at z= +/- 1.96

–Figure 6.4 (p.147)

–Boundaries set at z= +/- 1.96 provide objective criteria for deciding whether a treated individual is noticeably different from the original population.