Download Topics of the top of my head: • Population • Sample • Sample

Topics of the top of my head:
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Population
Sample
Sample statistics
 Sample mean = 𝑥̅ = …..
and 𝑝̂ = ….
 Mode =
 Median =
 Sample variance = …..
 Sample standard deviation = s = …..
 Quartiles =
 Percentiles =
 Range =
 Inter-quartile range
Statistic
Parameter
Random sample
Random variable
Probability
Conditional Probabilities
Multiplicative rule for independent events
Multiplicative rule for joint event
Additive rule for mutually exclusive events
Distributions of
 Population
 Data
 Sampling for a statistic
Graphing
 Pie chart
 Bar chart
 Histogram
 Dot plot
 Stem n leaf
 Series plot (line plot)
Proportions (dichotomous events, two categories)
 Mean = p
 Variance = p(1-p)
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Std = √𝑝(1 − 𝑝)
Binomial (counts out of n independent trials)
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𝑛!
𝑦!(𝑛−𝑦)!
𝑝 𝑦 (1 − 𝑝)(𝑛−𝑦)
 Mean = np
 Variance = np(1-p)
 Std = √𝑛𝑝(1 − 𝑝)
Normal distribution
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𝑃(𝑦) =
f(y) =
1
√2𝜋𝜎 2
1 (𝑦−𝜇)2
)
𝜎2
exp(-2
 mean = μ
 variance = 𝜎 2
 std = σ
Normal approximation of 𝑝̂ if np>15 and n(1-p)>15
Sampling distribution
 Mean=population mean, which is either
 μ general
 p
binary/dichotomous
 np count
 Variance = population variance/sample size, which is either
 𝜎 2 /n
general
 p(1-p)/n
binary/dichotomous
 np(1-p)/n count
Central Limit Theorem: If n is large, sampling distribution of mean is approximately normal
regardless of shape of population distribution.
Confidence intervals
68/95/99.7 or 1/2/3 rule
Standard score z = (x- 𝑥̅ )/n
 mean=0
 std=1
 uses (comparing distributions, for looking up in tables, testing hypotheses)
Shapes of distributions
 Left skew
 Right skew
 Uni-modal
 Symmetric
 Bi-modal
Type of decisions and
 Alpha
 Beta
 Power
 Type I error
 Type II error
5 Steps of a hypothesis test
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(1.) Assumptions
(2) Hypotheses
(3) Test statistic
(4) P-value
(5) Conclusion ( & interpretation in context of problem)
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Using all of the above to make inferences from sample about population.
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Basic R:
 Assignment: < Inputting sample data sets: c(x1,x2,….,xn) where c is for “combining” or
“concatenation”
 Addition: x + p
 Subtractions: x - p
 Multiplication: x*p
 Division: x/n
 Square root: sqrt(y)
 Finding sum of values: sum(x)
 Mean: mean(x)
 Standard deviation: sd(x)
 Z-scores: scale(x)
 Finding probabilities from normal: P(Y<y) = pnorm(y,mean= , sd= )
 Finding quanitles from normal : y = qnorm(p,mean=,sd=)
 Finding probabilities from binomial: P(Y<y) = pbinom(y,n,p)
 Finding quantiles from binomial:
y = qbinom(p,y,n)
 Test of proportions (binomial counts):
proportion.test(y,n,𝑝𝑜, , alternative=”two.sided”, conf.level=alpha,
correct=FALSE)
or alternative = “left” or “right”