Note on Condition of T-test used

  • Note
  • Things to remember

Test of significance of a single mean.

Under H0, the test statistic is.



and it followa students t-distribution with (n-1)degree of freedom


$$S^2=an\,unbiased\,estimate\,of\,the\,population\,varience\,and\,it\,is\,computed by$$

1. Actual mean method.



This is application when the mean value is in whole number.

2.Direct method.




This is applicable when the mean value is in fractional form and the data are given at most two digits.

3. Shortcut or assumed mean method




when the biased estimate of the population variance i,e s2 or standard deviation 's' given then the value of t is computed by.






Test of significance of a difference between two means.

Under the assumption thatσ12222 i,e population variances are equal but unknown the test statistics under H012 is

i,e the test statistic t follows t-distribution with n1+n2-Z degree of freedom.





Kerlinger, F.N. Foundation of Behavioural Research. New Delhi: Surjeet Publication, 2000.

Kothari, C.R. Research Methodology. India: Vishwa Prakashan, 1990.

Singh, M.L. and J.M Singh. Understanding Research Methodology. 1998.

Singh, Mrigendra Lal. Understanding Research Methodology. Nepal: National Book centre, 2013.

  1. $$t=\frac{Difference}{S.E\overline{(X)}}$$

  2. $$\frac{\overline{X}-µ}{\frac{s}{\sqrt{n}}}$$

  3. $$\frac{\overline{X}-µ}{\sqrt{\frac{s^2}{n}}}∼t_n=1$$


Very Short Questions



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