t Statistic of Normal Distribution Calculator

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✖Sample Mean is the arithmetic average of the individual values in the given sample from a population.ⓘ Sample Mean [x̄]			+10% -10%
✖Population Mean is the arithmetic average of the individual values in the given population from which the samples are taking.ⓘ Population Mean [μ]			+10% -10%
✖Sample Standard Deviation is the square root of expectation of the squared deviation of the random variable associated with the given sample from a population from its sample mean.ⓘ Sample Standard Deviation [s]			+10% -10%
✖Sample Size is the total number of individuals present in the given sample in a population under investigation.ⓘ Sample Size [N]			+10% -10%

✖t Statistic of Normal Distribution is the standard parameter that characterize a sample from population using the sample mean and population mean with respect to the sample standard deviation.ⓘ t Statistic of Normal Distribution [t_Normal]

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t Statistic of Normal Distribution

Formula

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

Example

`"5.111013"=("26"-"22")/("3.5"/sqrt("20"))`

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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 - Square root function, sqrt(Number)

Variables Used

t Statistic of Normal Distribution - t Statistic of Normal Distribution is the standard parameter that characterize a sample from population using the sample mean and population mean with respect to the sample standard deviation.
Sample Mean - Sample Mean is the arithmetic average of the individual values in the given sample from a population.
Population Mean - Population Mean is the arithmetic average of the individual values in the given population from which the samples are taking.
Sample Standard Deviation - Sample Standard Deviation is the square root of expectation of the squared deviation of the random variable associated with the given sample from a population from its sample mean.
Sample Size - Sample Size is the total number of individuals present in the given sample in a population under investigation.

STEP 1: Convert Input(s) to Base Unit

Sample Mean: 26 --> No Conversion Required
Population Mean: 22 --> No Conversion Required
Sample Standard Deviation: 3.5 --> No Conversion Required
Sample Size: 20 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_Normal = (x̄-μ)/(s/sqrt(N)) --> (26-22)/(3.5/sqrt(20))

Evaluating ... ...

t_Normal = 5.11101251999952

STEP 3: Convert Result to Output's Unit

5.11101251999952 --> No Conversion Required

FINAL ANSWER

5.11101251999952 ≈ 5.111013 <-- t Statistic of Normal Distribution

(Calculation completed in 00.001 seconds)

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Created by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 16 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

F Value of Two Samples

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

Range of Data given Largest and Smallest Items

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

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

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 standard parameter that characterize a sample from population using the sample mean and population mean with respect to the sample standard deviation. 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 -> 5.111013 = (26-22)/(3.5/sqrt(20)).

FAQ

What is t Statistic of Normal Distribution?

t Statistic of Normal Distribution formula is defined as the standard parameter that characterize a sample from population using the sample mean and population mean with respect to the sample standard deviation 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 arithmetic average of the individual values in the given sample from a population, Population Mean is the arithmetic average of the individual values in the given population from which the samples are taking, Sample Standard Deviation is the square root of expectation of the squared deviation of the random variable associated with the given sample from a population from its sample mean & Sample Size is the total number of individuals present in the given sample in a population under investigation.

How to calculate t Statistic of Normal Distribution?

t Statistic of Normal Distribution formula is defined as the standard parameter that characterize a sample from population using the sample mean and population mean with respect to the sample standard deviation 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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