t Statistic of Normal Distribution Calculator

✖Sample Mean is the average value of all the data points in a specific sample.ⓘ Sample Mean [x̄]			+10% -10%
✖Population Mean is the average value of all the values in a population.ⓘ Population Mean [μ]			+10% -10%
✖Sample Standard Deviation is the measure of how much the values in a specific sample vary.ⓘ Sample Standard Deviation [s]			+10% -10%
✖Sample Size is the total number of individuals or items included in a specific sample.ⓘ Sample Size [N]			+10% -10%

✖t Statistic of Normal Distribution is the t statistic calculated from a normal distribution.ⓘ t Statistic of Normal Distribution [t_Normal]

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Formula

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t Statistic of Normal Distribution

Formula

`"t"_{"Normal"} = ("x̄"-"μ")/("s"/sqrt("N"))`

Example

`"4.21637"=("48"-"28")/("15"/sqrt("10"))`

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t Statistic of Normal Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size))
t_Normal = (x̄-μ)/(s/sqrt(N))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

t Statistic of Normal Distribution - t Statistic of Normal Distribution is the t statistic calculated from a normal distribution.
Sample Mean - Sample Mean is the average value of all the data points in a specific sample.
Population Mean - Population Mean is the average value of all the values in a population.
Sample Standard Deviation - Sample Standard Deviation is the measure of how much the values in a specific sample vary.
Sample Size - Sample Size is the total number of individuals or items included in a specific sample.

STEP 1: Convert Input(s) to Base Unit

Sample Mean: 48 --> No Conversion Required
Population Mean: 28 --> No Conversion Required
Sample Standard Deviation: 15 --> No Conversion Required
Sample Size: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_Normal = (x̄-μ)/(s/sqrt(N)) --> (48-28)/(15/sqrt(10))

Evaluating ... ...

t_Normal = 4.21637021355784

STEP 3: Convert Result to Output's Unit

4.21637021355784 --> No Conversion Required

FINAL ANSWER

4.21637021355784 ≈ 4.21637 <-- t Statistic of Normal Distribution

(Calculation completed in 00.004 seconds)

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< 18 Basic Formulas in Statistics Calculators

P Value of Sample

Go P Value of Sample = (Sample Proportion-Assumed Population Proportion)/sqrt((Assumed Population Proportion*(1-Assumed Population Proportion))/Sample Size)

Sample Size given P Value

Go Sample Size = ((P Value of Sample^2)*Assumed Population Proportion*(1-Assumed Population Proportion))/((Sample Proportion-Assumed Population Proportion)^2)

t Statistic of Normal Distribution

Go t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size))

t Statistic

Go t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))

Chi Square Statistic

Go Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2)

Number of Classes given Class Width

Go Number of Classes = (Largest Item in Data-Smallest Item in Data)/Class Width of Data

Class Width of Data

Go Class Width of Data = (Largest Item in Data-Smallest Item in Data)/Number of Classes

Expectation of Difference of Random Variables

Go Expectation of Difference of Random Variables = Expectation of Random Variable X-Expectation of Random Variable Y

Chi Square Statistic given Sample and Population Variances

Go Chi Square Statistic = ((Sample Size-1)*Sample Variance)/Population Variance

Expectation of Sum of Random Variables

Go Expectation of Sum of Random Variables = Expectation of Random Variable X+Expectation of Random Variable Y

Number of Individual Values given Residual Standard Error

Go Number of Individual Values = (Residual Sum of Squares/(Residual Standard Error of Data^2))+1

F Value of Two Samples given Sample Standard Deviations

Go F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2

Mid Range of Data

Go Mid Range of Data = (Maximum Value of Data+Minimum Value of Data)/2

F Value of Two Samples

Go F Value of Two Samples = Variance of Sample X/Variance of Sample Y

Smallest Item in Data given Range

Go Smallest Item in Data = Largest Item in Data-Range of Data

Largest Item in Data given Range

Go Largest Item in Data = Range of Data+Smallest Item in Data

Range of Data

Go Range of Data = Largest Item in Data-Smallest Item in Data

Relative Frequency

Go Relative Frequency = Absolute Frequency/Total Frequency

t Statistic of Normal Distribution Formula

t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size))
t_Normal = (x̄-μ)/(s/sqrt(N))

What is the t test in Statistics?

A t test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another. There are three t tests to compare means: a one-sample t test, a two-sample t test and a paired t test.

How to Calculate t Statistic of Normal Distribution?

t Statistic of Normal Distribution calculator uses t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size)) to calculate the t Statistic of Normal Distribution, t Statistic of Normal Distribution formula is defined as the the t statistic calculated from a normal distribution. t Statistic of Normal Distribution is denoted by t_Normal symbol.

How to calculate t Statistic of Normal Distribution using this online calculator? To use this online calculator for t Statistic of Normal Distribution, enter Sample Mean (x̄), Population Mean (μ), Sample Standard Deviation (s) & Sample Size (N) and hit the calculate button. Here is how the t Statistic of Normal Distribution calculation can be explained with given input values -> 4.21637 = (48-28)/(15/sqrt(10)).

FAQ

What is t Statistic of Normal Distribution?

t Statistic of Normal Distribution formula is defined as the the t statistic calculated from a normal distribution and is represented as t_Normal = (x̄-μ)/(s/sqrt(N)) or t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size)). Sample Mean is the average value of all the data points in a specific sample, Population Mean is the average value of all the values in a population, Sample Standard Deviation is the measure of how much the values in a specific sample vary & Sample Size is the total number of individuals or items included in a specific sample.

How to calculate t Statistic of Normal Distribution?

t Statistic of Normal Distribution formula is defined as the the t statistic calculated from a normal distribution is calculated using t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size)). To calculate t Statistic of Normal Distribution, you need Sample Mean (x̄), Population Mean (μ), Sample Standard Deviation (s) & Sample Size (N). With our tool, you need to enter the respective value for Sample Mean, Population Mean, Sample Standard Deviation & Sample Size and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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