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Sampling & Experiments
Interpretations
Important Things You May Have Forgotten
Probability Table
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100

Why is it important to RANDOMLY ASSIGN TREATMENTS?

Random assignment = causation. 

In order to say explanatory CAUSED response

100
P-value = 0.001
What is "since the P-value is less than any reasonable significance level, we reject the null hypothesis, and conclude there is significance evidence to support the alternative hypothesis"?
100
How to identify outliers for univariate data
What is Q1 - 1.5(IQR) and Q3 + 1.5(IQR)?
100

P(Female)

52/100

100

What percentile is someone in with a z-score of +1.5

Normal(0,1) 

P(Z<1.5) = 93rd percentile

200
A common form of blocking for comparing just two treatments.
What is matched pairs?
200

The slope in the least-square regression line, y-hat = 15 - 4x. y-hat = predicted BEAT points. x = # of referrals

"For every 1 referral, the number of BEAT points is predicted to decrease by 4"

200

Why is it important to select a random SAMPLE?

Random Sampling = generalization 

In order to generalize results to population from which sample was taken

200

Are Male and Football independent?

P(Football) = 33/100 = 33%

P(Football | Male) = 20/48 = 42%

NOT INDEPENDENT. Liking football becomes more likely if you are a male

200

The probability of at least 8 successes in 12 trials given a probability of success of 45%.

BINOM(n=12, p = 0.45)

P(X>8) =0.11

300
When some groups in the population are left out of the process of choosing a sample
What is undercoverage?
300
A z-score of -3.45
What is "The data value is 3.45 standard deviations below the mean"?
300

Mean > Median. What is the shape of the distribution?

Skewed to the right!!!!

Mean follows direction of the skew

300

P(Male and Football)

20/100

300

The z* for a 92% confidence interval

N(0, 1)

P(BETWEEN) = 0.92

1.75

400
The population is divided into groups. Some groups are randomly selected and all individuals in the chosen groups are sampled.
What is cluster sampling?
400

95% confidence interval = (0.52, 0.62)

We are 95% confident that the true proportion of {CONTEXT} is between 52% and 62%

400

Distribution A = N(5, 10)

Distribution B = 2A + 1

Describe Distribution B

Normal 

Mean = 2(5) + 1 = 11

SD = 2(10) = 20

400

P(Male | Football)

20/33

400

95% Confidence Interval for proportion of students who came late to school. Sample of 50 students had 20% of them come late. 

One proportion z-interval

x = 10, n = 50, CL = 0.95

(0.09, 0.31)

500

Steps to selecting a random sample of 30 students out of a class of 200

Assign each student a unique number 1-200

Use RNG to select 30 numbers between 1-200 (no repeats)

Sample those students whose numbers were chosen

500
The 95% confidence interval (-4.25, -1.33) for the difference of two means (mean #1 - mean #2).
What is "With 95% confidence, we estimate that mean #1 is between 4.25 and 1.33 units less than mean #2"
500

What are the conditions for inference of MEANS?

Random sample!

Independence: n<0.10(N)

Normal: n>30 

(for proportions its np >10, n(1-p)>10)

500

P(Male Or Football)

(48+33 - 20) / 100

500

Probability of a person being left handed is 10%. What is the probability you will find THE FIRST left handed person on the 3rd person you ask?

GEOMETRIC(p=0.1)

P(X = 3) = 0.081