If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

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 before checking your answers with the calculators.
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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
• $\alpha$ = level of significance or significance level
• zα/2 = critical z value separating an area or probability of α⁄2 in the right tail
• -zα/2 = critical z value separating an area or probability of α⁄2 in the left tail
• zα = critical z value separating an area or probability of α in the right tail
• -zα = 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
• SEest = 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
• s2 = sample variance
• σ = population standard deviation
• σ2 = population variance
• tα/2 = critical t value separating an area or probability of α⁄2 in the right tail (use for one-tailed tests)
• tα = critical t value separating an area or probability of α in the right tail (use for two-tailed tests)
• df = degrees of freedom
• Χ2 = Chi-Square distribution
• Χ2R = right-tailed (upper-tail) critical values of the Chi-Square distribution
• Χ2L = 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, zα/2
• Requirements: population is normally distributed OR $n \gt 30$; AND $\sigma$ is given

in

• Given: α
To Find: CL, zα/2
• Requirements: population is normally distributed OR $n \gt 30$; AND $\sigma$ is given

in

• Given: CL, df
To Find: α, critical t
• Requirements: population is normally distributed OR $n \gt 30$ AND s is given

in

• Given: α, df
To Find: CL, critical t
• Requirements: population is normally distributed OR $n \gt 30$ AND s is given

in

• Given: CL, n
To Find: α, critical t
• Requirements: population is normally distributed OR $n \gt 30$ AND s is given

in

• Given: α, n
To Find: CL, critical t
• Requirements: population is normally distributed OR $n \gt 30$ AND s is given

in

• Given: CL, df
To Find: α, critical Χ2
• Requirements: population is normally distributed

in

• Given: α, df
To Find: CL, critical Χ2
• Requirements: population is normally distributed

in

## 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

in

in

• Given: CL, x, n
To Find: p̂, q̂, E, CI
• Requirements: np̂ ≥ 5, nq̂ ≥ 5, np̂q̂ ≥ 10

in

• Given: CL, p̂, E
To Find: q̂, n
• in

in

in

• Given: CL, E
To Find: n
• in

in

• Given: zα/2, p̂, E
To Find: q̂, n
• in

in

• Given: zα/2, E
To Find: n
• in

• Given: p̂, E, CL (Use 95% if not given)
To Find: CI
• in

in

## Estimating Population Mean

• Given: CI
To Find: x̄, E

• Given: x̄, E, CL (Use 95% if not given)
To Find: CI
• in

• Given: CL, σ, n, x̄
To Find: E, CI
• When requirements are met: population is normally distributed OR $n \gt 30$

in

• Given: CL, s, n, x̄
To Find: E, CI
• When requirements are met: population is normally distributed OR $n \gt 30$

in

• Given: σ, CL, E
To Find: n
• in

in

• Given: s, CL, df, E
To Find: n
• in

in

• Given: min, max, α, E, sample size
To Find: R, s, df, n
• in

in

• Given: min, max, CL, E
To Find: R, σ, n
• in

in

• Given: Raw Dataset (from Sample)
To Find: x̄, s

## Estimating Population Variance and Population Standard Deviation

• Given: CL, n, s
To Find: df, Χ2L, Χ2R, CI
• in

## Expected Counts

• Given: i, pi, n
To Find: Ei