T-distribution is the most famous theoretical probability distribution in continuous family of distributions. T distribution is used in estimation where normal distribution cannot be used to estimate population parameters. Copy the link given below and paste it in new browser window to get more information on T distribution:- http://www.transtutors.com/homework-help/statistics/t-distribution.aspx

1. T-distribution

2. What is T-distribution?
 T distribution is theoretical distribution that arises from
sampling from normal distribution
 Discovered by William S Gosset in 1908 and published under
penname ‘Student’ in Biometrika.
 Best for estimation of population mean when sample size is
small and population standard deviation is unknown

3. Specifics of T-distribution
PDF:
Mean = 0
Median = 0
Mode = 0
Variance = n / (n-2)
Skewness coefficient = 0
Kurtosis coefficient = 6 / (n-4)
2
1
2
1
2
,
2
1
1
)(
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













n
n
x
n
Bn
xf

4. T-Distribution vs
Normal Distribution
T distribution Normal distribution
More spread Less spread
More area in tails Less area in tails
Less area in centre More area in centre
Used for small n Used for large n
Population standard deviation
is unknown
Population standard deviation
is known

5. T-distribution Curve in
comparison with Normal Curve

6. Determination of T-table
critical values
Critical value tables are available for specified level of significance
and degrees of freedom.

7. Application of t-tests
 Test for single sample mean
 Independent samples t test
 Dependent sample t test
 Test for correlation coefficient

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