One sample t test (Two Sides)

October 23rd, 2011 by rory | Filed under Statistics.

One sample t test (two sided) was used to determine whether the average value of a sample of the same or significantly different with a value comparison. T test is used if the number of sample data under 30.

Hypothesis:

H_{o}:\mu =\mu _{o}

H_{1}:\mu \neq \mu _{o}

Statistic Test:
t = \frac{\overline{x}-\mu _{o}}{s/\sqrt{n}}

Decision Making:
Decision making is based on a comparison of t count and t tables. If t count exceeds than t_{\alpha /2,v}  or less than -t_{\alpha /2,v}  then Ho is rejected. Whereas if t count is between -t_{\alpha /2,v}  and t_{\alpha /2,v}  the Ho accepted.

Note:

  • \alpha  is the significance level obtained from figure 1 minus the confidence level. Usually the level of trust that is often used is 95%, so the significance level (\alpha ) = 1-95% = 5% or 0.05.
  • v is the degrees of freedom, which is obtained from the number of data samples (n) minus 1.
  • From values \alpha  ??and degrees of freedom (v) t values ??can be obtained tables that can be seen in the t distribution table.

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