Calculating probabilities
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1 Calculating probabilities Prof. Jacob M. Montgomery Quantitative Political Methodology (L32 363) September 19, 2016 Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
2 Class business Under resource on website Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
3 Class business Under resource on website HW 2 Due Wednesday. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
4 Class business Under resource on website HW 2 Due Wednesday. PS3 will be due on 10/5 Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
5 Class business Under resource on website HW 2 Due Wednesday. PS3 will be due on 10/5 Questions? Concerns? Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
6 Learning objectives for today How to find probabilities from a binomial table Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
7 Learning objectives for today How to find probabilities from a binomial table How to find probabilities using a Z-distribution table Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
8 Learning objectives for today How to find probabilities from a binomial table How to find probabilities using a Z-distribution table How to find critical values. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
9 Learning objectives for today How to find probabilities from a binomial table How to find probabilities using a Z-distribution table How to find critical values. Extend this logic to the t-distribution (online only) Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
10 Learning objectives for today How to find probabilities from a binomial table How to find probabilities using a Z-distribution table How to find critical values. Extend this logic to the t-distribution (online only) We will return to sampling distributions on Monday Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
11 Motivation Castenedat v. Partida The true number of Mexican-Americans was 79.1% of the population. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
12 Motivation Castenedat v. Partida The true number of Mexican-Americans was 79.1% of the population. Individuals were selected for jury participation using the key man system. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
13 Motivation Castenedat v. Partida The true number of Mexican-Americans was 79.1% of the population. Individuals were selected for jury participation using the key man system. 45.5% of the members of the grand jury were Mexican-American. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
14 Motivation Castenedat v. Partida The true number of Mexican-Americans was 79.1% of the population. Individuals were selected for jury participation using the key man system. 45.5% of the members of the grand jury were Mexican-American. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
15 Motivation Castenedat v. Partida The true number of Mexican-Americans was 79.1% of the population. Individuals were selected for jury participation using the key man system. 45.5% of the members of the grand jury were Mexican-American. How likely was this to happen by chance if the jury was of size n = 60? Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
16 Question 1 Which fraction represents the probability of obtaining exactly eight heads in ten tosses of a fair coin? If you dont have the means to calculate the probability, at least set up the equation correctly. Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
17 Question 2 For a normal distribution with µ = 50 and σ = 3, find the probability that an observation falls: At or below the value of 56 Between the values of 45 and 56 Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
18 Question 3 Suppose that for exam grades µ = 75 and σ = 15. What is the probability of receiving an exam grade of 90 or better? What about a 60 or worse? If the probability of doing better than you is.05, then what is your score? Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
19 Question 4 (not on your form) If you have a t-distributed variable with 21 degres of freedom. What is the probability of a value above 1.721?.05% of the distribution is greater than what critical value? Lecture 6 (QPM 2016) Calculating probabilities September 19, / 8
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