If there is one prayer that you should

- Samuel Dominic Chukwuemeka
**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.

JESUS CHRIST is the same yesterday, and today, and forever.

- Hebrews 13:8

The

- Samuel Chukwuemeka**Joy** of a **Teacher** is the **Success** of his **Students.**

I greet you this day,

You may use these calculators to check your answers. You are encouraged to solve the questions first before checking
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Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.

Should you need to contact me, please use the form at the bottom of the page. Thank you for visiting.

**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
- 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)

__Given__: CL

__To Find__: α, z_{α/2}

__Given__: α

__To Find__: CL, z_{α/2}

__Given__: CL, df

__To Find__: α, critical t

__Given__: α, df

__To Find__: CL, critical t

__Given__: CL, n

__To Find__: α, critical t

__Given__: α, n

__To Find__: CL, critical t

__Given__: CL, df

__To Find__: α, critical Χ^{2}

__Given__: α, df

__To Find__: CL, critical Χ^{2}

__Given__: CI

__To Find__: p̂, E

__Given__: CI, n

__To Find__: p̂, E, x

__Given__: p̂, n, CL

__To Find__: q̂, E, CI

__Given__: CL, x, n

__To Find__: p̂, q̂, E, CI

__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

__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

__Given__: CL, s, n, x̄

__To Find__: E, CI

__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

__Given__: CL, n, s

__To Find__: df, Χ^{2}_{L}, Χ^{2}_{R}, CI

__Given__: i, p_{i}, n

__To Find__: E_{i}