JESUS CHRIST is the same yesterday, and today, and forever. - Hebrews 13:8
The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka
Inferential Statistics Calculators
I greet you this day,
You may use these calculators to check your answers. You are encouraged to solve the questions first, and check your answers. These topics are covered in my
Videos and
Notes on Inferential Statistics.
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Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S
Symbols and Meanings
CL = confidence level or level of confidence or degree of confidence or confidence coefficient
CI = confidence interval or interval estimate
α = level of significance or significance level
z_{α/2} = critical z value separating an area or probability of ^{α}⁄2 in the right tail
-z_{α/2} = critical z value separating an area or probability of ^{α}⁄2 in the left tail
z_{α} = critical z value separating an area or probability of α in the right tail
-z_{α} = critical z value separating an area or probability of α in the left tail
p̂ = sample proportion or estimated proportion of successes
q̂ = estimated proportion of failures
p = population proportion
SE = standard error
SE_{est} = estimated standard error
x = number of individuals in the sample with the specified characteristic
n = sample size
N = population size
E = margin of error or maximum error of estimation or error bound
x̄ = sample mean
μ = population mean
s = sample standard deviation
s^{2} = sample variance
σ = population standard deviation
σ^{2} = population variance
t_{α/2} = critical t value separating an area or probability of ^{α}⁄2 in the right tail (use for one-tailed tests)
t_{α} = critical t value separating an area or probability of α in the right tail (use for two-tailed tests)
df = degrees of freedom
Χ^{2} = Chi-Square distribution
Χ^{2}_{R} = right-tailed (upper-tail) critical values of the Chi-Square distribution
Χ^{2}_{L} = left-tailed (lower-tail) critical values of the Chi-Square distribution
CI for Population Proportion in Plus-Minus Notation = p̂ ± E
CI for Population Proportion in Interval Notation = (p̂ - E, p̂ + E)
CI for Population Proportion in Trilinear Inequality = p̂ - E < p < p̂ + E
CI for Population Mean in Plus-Minus Notation = x̄ ± E
CI for Population Mean in Interval Notation = (x̄ - E, x̄ + E)
CI for Population Mean in Trilinear Inequality = x̄ - E < μ < x̄ + E
min = minimum data value
max = maximum data value
R = range (we shall use it typically for the Range Rule of Thumb)
Critical Values
Given: CL
To Find: α, z_{α/2}
Requirements: population is normally distributed or n > 30 and σ is given
Given: α
To Find: CL, z_{α/2}
Requirements: population is normally distributed or n > 30 and σ is given
Given: CL, df
To Find: α, critical t
Requirements: population is normally distributed or n > 30 and s is given
Given: α, df
To Find: CL, critical t
Requirements: population is normally distributed or n > 30 and s is given
Given: CL, n
To Find: α, critical t
Requirements: population is normally distributed or n > 30 and s is given
Given: α, n
To Find: CL, critical t
Requirements: population is normally distributed or n > 30 and s is given
Given: CL, df
To Find: α, critical Χ^{2}
Requirement: population is normally distributed
Given: α, df
To Find: CL, critical Χ^{2}
Requirement: population is normally distributed
Estimating Population Proportion
Given: CI
To Find: p̂, E
Given: CI, n
To Find: p̂, E, x
Given: p̂, n, CL
To Find: q̂, E, CI
Requirements: np̂ ≥ 5, nq̂ ≥ 5, np̂q̂ ≥ 10
Given: CL, x, n
To Find: p̂, q̂, E, CI
Requirements: np̂ ≥ 5, nq̂ ≥ 5, np̂q̂ ≥ 10
Given: CL, p̂, E
To Find: q̂, n
Given: CL, E
To Find: n
Given: z_{α/2}, p̂, E
To Find: q̂, n
Given: z_{α/2}, E
To Find: n
Given: p̂, E, CL (Use 95% if not given)
To Find: CI
Estimating Population Mean
Given: CI
To Find: x̄, E
Given: x̄, E, CL (Use 95% if not given)
To Find: CI
Given: CL, σ, n, x̄
To Find: E, CI
When requirements are met: population is normally distributed or n > 30
Given: CL, s, n, x̄
To Find: E, CI
When requirements are met: population is normally distributed or n > 30
Given: σ, CL, E
To Find: n
Given: s, CL, df, E
To Find: n
Given: min, max, α, E, sample size
To Find: R, s, df, n
Given: min, max, CL, E
To Find: R, σ, n
Given: Raw Dataset (from Sample)
To Find: x̄, s
Estimating Population Variance and Population Standard Deviation