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.

For in GOD we live, and move, and have our being.

- Acts 17:28

The

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

I greet you this day:

**First:** Read the notes.

**Second:** View the videos.

**Third:** Solve the questions/solved examples.

**Fourth:** Check your solutions with my **thoroughly-explained** solutions.

**Fifth:** Check your solutions with the **calculators** as applicable.

**
If you are doing multiple calculations, you may need to refresh your browser after each calculation, in order to clear
all previous results.
**

These are what I have at the moment. I intend to add more functionalities as time demands.

Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.

If you are my student, please do not contact me here. Contact me via the school's system. Thank you.

**Samuel Dominic Chukwuemeka** (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

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Given: CL
To Find: α, -z_{α/2}
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Given: α
To Find: CL, -z_{α/2}
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Given: p, p̂, α
Test hypothesis using Classical Approach and P-value Approach
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Given: p, n, x, α
Test hypothesis using Classical Approach and P-value Approach
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Given: p, n, x of a Binomial Distribution; α
Test hypothesis using P-value Approach
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Given: CL
To Find: α, z_{α}
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Given: α
To Find: CL, z_{α}
**

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Given: p, p̂, α
Test hypothesis using Classical Approach and P-value Approach
**

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Given: p, n, x, α
Test hypothesis using Classical Approach and P-value Approach
**

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Given: p, n, x of a Binomial Distribution; α
Test hypothesis using P-value Approach
**

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Given: σ, x, n, p
Test hypothesis using the Classical Approach and the P-value Approach
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Given:p, p̂, α
Test hypothesis using Classical Approach and P-value Approach
**

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Given: CL, x, n, p
Test hypothesis using the Confidence Interval Method
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Given: p, n, x of a Binomial Distribution; α
Test hypothesis using P-value Approach
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Given: x_{1}, n_{1}, x_{2}, n_{2}, α **

Test hypothesis using Classical Approach and P-value Approach

__Given__: x_{1}, n_{1}, x_{2}, n_{2}, α

Test hypothesis using Classical Approach and P-value Approach

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Given: σ, x, n, p
Test hypothesis using Classical Approach and P-value Approach
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Given: x_{1}, n_{1}, x_{2}, n_{2}, α **

To: Construct a confidence interval for p_{1} - p_{2}

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Given: CL, df
To Find: α, critical t
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Given: α df
To Find: CL, critical t
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Given: CL, n
To Find: α, critical t
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Given: α, n
To Find: CL, critical t
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Given: Raw dataset $X$ (from Sample)
To calculate: sample size, mean, standard deviation
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Given: sample size, test statistic
To Calculate: degrees of freedom, P-value
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Given: μ_{x̄}, x̄, s, n, α **

Test hypothesis using Classical Approach and P-value Approach

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Given: μ_{x̄}, x̄, σ, n, α **

Test hypothesis using Classical Approach and P-value Approach

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Given: CL, df
To Find: α, critical t
**

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Given: α df
To Find: CL, critical t
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Given: CL, n
To Find: α, critical t
**

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Given: α, n
To Find: CL, critical t
**

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Given: Raw dataset $X$ (from Sample)
To calculate: sample size, mean, standard deviation
**

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Given: sample size, test statistic
To Calculate: degrees of freedom, P-value
**

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Given: μ_{x̄}, x̄, s, n, α **

Test hypothesis using Classical Approach and P-value Approach

**
Given: μ_{x̄}, x̄, σ, n, α **

Test hypothesis using Classical Approach and P-value Approach

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Given: CL, df
To Find: α, critical t
**

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Given: α df
To Find: CL, critical t
**

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Given: CL, n
To Find: α, critical t
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Given: α, n
To Find: CL, critical t
**

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Given: Raw dataset $X$ (from Sample)
To calculate: sample size, mean, standard deviation
**

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Given: sample size, test statistic
To Calculate: degrees of freedom, P-value
**

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Given: μ_{x̄}, x̄, s, n, α **

Test hypothesis using Classical Approach and P-value Approach

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Given: μ_{x̄}, x̄, s, n, CL **

Test Hypothesis using the Confidence Interval Method

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Given: μ_{x̄}, x̄, σ, n, α **

Test hypothesis using Classical Approach and P-value Approach

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Given: Raw datasets $X_1$ and $X_2$ (Samples)
To Calculate: sample sizes, sample means, sample standard deviations, degrees of freedom
(several ones: use whatever is applicable)
Use for Independent Samples
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Given: Raw datasets $X_1$ and $X_2$ (Samples)
To Calculate: differences between values; sample size, sample mean, and sample standard
deviation of the difference, degrees of freedom
Use for Dependent Samples
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Given: x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, α **

Where: σ_{1} and σ_{2} are unknown, and are assumed to be equal

Pooled Sample Variance is used

Test hypothesis using Classical Approach and P-value Approach

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Given: x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, CL **

Where: σ_{1} and σ_{2} are unknown, and are not assumed to be equal

Pooled Sample Variance is used

Construct a confidence interval for μ_{1} - μ_{2}

Test hypothesis using Classical Approach and P-value Approach

Construct a confidence interval for μ

__Given__: Raw datasets $X_1$ and $X_2$ (Samples)

__To Calculate__: sample sizes, sample means, sample standard deviations, degrees of freedom
(several ones: use whatever is applicable)

Use for Independent Samples

__Given__: Raw datasets $X_1$ and $X_2$ (Samples)

__To Calculate__: differences between values; sample size, sample mean, and sample standard
deviation of the difference, degrees of freedom

Use for Dependent Samples

__Given:__ x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, α

__Where:__ σ_{1} and σ_{2} are unknown, and are assumed to be equal

Pooled Sample Variance is used

Test hypothesis using Classical Approach and P-value Approach

__Given:__ x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, CL

__Where:__ σ_{1} and σ_{2} are unknown, and are not assumed to be equal

Pooled Sample Variance is used

Construct a confidence interval for μ_{1} - μ_{2}

Test hypothesis using Classical Approach and P-value Approach

Construct a confidence interval for μ

**
Given: Raw datasets $X_1$ and $X_2$ (Samples)
To Calculate: sample sizes, sample means, sample standard deviations, degrees of freedom
(several ones: use whatever is applicable)
**

**
Given: x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, α **

Where: σ_{1} and σ_{2} are unknown, and are assumed to be equal

Pooled Sample Variance is used

Test hypothesis using Classical Approach and P-value Approach

__Given:__ x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, CL

__Where:__ σ_{1} and σ_{2} are unknown, and are not assumed to be equal

Pooled Sample Variance is used

Construct a confidence interval for μ_{1} - μ_{2}

**
Given: x̄_{1}, x̄_{2}, s_{1}, s_{2}, n_{1},
n_{2}, α **

Where: σ_{1} and σ_{2} are unknown, and are not assumed to be equal

Test hypothesis using Classical Approach and P-value Approach

Construct a confidence interval for μ

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Given: n, s, σ, α
Test hypothesis using Classical Approach and P-value Approach
**

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Given: Raw dataset $X$ (from Sample)
To Calculate: sample size, sample standard deviation
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Given: n, s, σ, α
Test hypothesis using Classical Approach and P-value Approach
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Given: Raw dataset $X$ (from Sample)
To Calculate: sample size, sample standard deviation
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Given: n, s, σ, α
Test hypothesis using Classical Approach and P-value Approach
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Given: n, s, σ, CL
Test Hypothesis using the Confidence Interval Method
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Given: Raw dataset $X$ (from Sample)
To Calculate: sample size, sample standard deviation
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Given: CL, df
To Find: α, critical Chi-Square
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Given: α, df
To Find: CL, critical Chi-Square
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Given: OV, EV
To Calculate: df, Χ^{2} (Show all steps), P-value
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Given: $OV$, Probabilities, Total Number of Trials
OR
Given: Benford's Law
To Calculate $EV$, $df$, $\chi^2$ (Show all steps), P-value
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Given: $OV$, $EV$, α (Use 5% if not specified)
Test Hypothesis Using Classical Approach and P-value Approach
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Given: $OV$, Probabilities, Total Number of Trials, α (Use 5% if not specified)
OR
Given: Benford's Law, α (Use 5% if not specified)
Test Hypothesis Using Classical Approach and P-value Approach
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Test of Independence: Sample Data: Right-Tailed

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Given: Contingency Table
Test for Independence using the Critical Value Method and the P-value Method
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Given: Datasets 1, 2, and 3
Calculate the F test statistic (Show all work)
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Given: Datasets 1, 2, and 3
Test Hypothesis Using Classical Approach and P-value Approach
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Given: datasets X and Y
Test hypothesis using the Critical Value Method and the P-value Method
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Given: datasets X and Y
Test hypothesis using the Critical Value Method and the P-value Method
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Given: datasets X and Y
Test hypothesis using the Critical Value Method and the P-value Method
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