## t Statistic Solution

STEP 0: Pre-Calculation Summary
Formula Used
t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))
t = (μObserved-μTheoretical)/(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 - t Statistic is the value obtained from a t-test, used to determine if there is a significant difference between the means of two groups.
Observed Mean of Sample - Observed Mean of Sample is the average value of the data points in a specific sample.
Theoretical Mean of Sample - Theoretical Mean of Sample is the expected average value of a sample, often based on theoretical calculations or assumptions.
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
Observed Mean of Sample: 64 --> No Conversion Required
Theoretical Mean of Sample: 42 --> 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 = (μObservedTheoretical)/(s/sqrt(N)) --> (64-42)/(15/sqrt(10))
Evaluating ... ...
t = 4.63800723491362
STEP 3: Convert Result to Output's Unit
4.63800723491362 --> No Conversion Required
4.63800723491362 4.638007 <-- t Statistic
(Calculation completed in 00.005 seconds)
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## < 18 Basic Formulas in Statistics Calculators

P Value of Sample
P Value of Sample = (Sample Proportion-Assumed Population Proportion)/sqrt((Assumed Population Proportion*(1-Assumed Population Proportion))/Sample Size)
Sample Size given P Value
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
t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size))
t Statistic
t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))
Chi Square Statistic
Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2)
Number of Classes given Class Width
Number of Classes = (Largest Item in Data-Smallest Item in Data)/Class Width of Data
Class Width of Data
Class Width of Data = (Largest Item in Data-Smallest Item in Data)/Number of Classes
Expectation of Difference of Random Variables
Expectation of Difference of Random Variables = Expectation of Random Variable X-Expectation of Random Variable Y
Chi Square Statistic given Sample and Population Variances
Chi Square Statistic = ((Sample Size-1)*Sample Variance)/Population Variance
Expectation of Sum of Random Variables
Expectation of Sum of Random Variables = Expectation of Random Variable X+Expectation of Random Variable Y
Number of Individual Values given Residual Standard Error
Number of Individual Values = (Residual Sum of Squares/(Residual Standard Error of Data^2))+1
F Value of Two Samples given Sample Standard Deviations
F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2
Mid Range of Data
Mid Range of Data = (Maximum Value of Data+Minimum Value of Data)/2
F Value of Two Samples
F Value of Two Samples = Variance of Sample X/Variance of Sample Y
Smallest Item in Data given Range
Smallest Item in Data = Largest Item in Data-Range of Data
Largest Item in Data given Range
Largest Item in Data = Range of Data+Smallest Item in Data
Range of Data
Range of Data = Largest Item in Data-Smallest Item in Data
Relative Frequency
Relative Frequency = Absolute Frequency/Total Frequency

## t Statistic Formula

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

t Statistic calculator uses t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size)) to calculate the t Statistic, t Statistic formula is defined as the value obtained from a t-test, used to determine if there is a significant difference between the means of two groups. t Statistic is denoted by t symbol.

How to calculate t Statistic using this online calculator? To use this online calculator for t Statistic, enter Observed Mean of Sample Observed), Theoretical Mean of Sample Theoretical), Sample Standard Deviation (s) & Sample Size (N) and hit the calculate button. Here is how the t Statistic calculation can be explained with given input values -> 10.54093 = (64-42)/(15/sqrt(10)).

### FAQ

What is t Statistic?
t Statistic formula is defined as the value obtained from a t-test, used to determine if there is a significant difference between the means of two groups and is represented as t = (μObservedTheoretical)/(s/sqrt(N)) or t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size)). Observed Mean of Sample is the average value of the data points in a specific sample, Theoretical Mean of Sample is the expected average value of a sample, often based on theoretical calculations or assumptions, 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?
t Statistic formula is defined as the value obtained from a t-test, used to determine if there is a significant difference between the means of two groups is calculated using t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size)). To calculate t Statistic, you need Observed Mean of Sample Observed), Theoretical Mean of Sample Theoretical), Sample Standard Deviation (s) & Sample Size (N). With our tool, you need to enter the respective value for Observed Mean of Sample, Theoretical Mean of Sample, 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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