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Table of Contents Statistical Tests Means One Sample t-Test Large Sample Size | |
See also: survey on statistical tests, small samples, two-sample t-test, distribution calculator |
The decision can be made according to the table below:
1. We have to formulate our two hypotheses (the null hypothesis H_{0} and the alternative hypothesis H_{1}):
H_{0}: amount <= limit H_{1}: amount > limit
3. In order to decide which of the two hypotheses is true we calculate the test statistic
,
which is normally distributed. The z value gives us the distance of the measured from the specified value µ in terms of the standard deviation s, e.g. when z=1.5, the distance is 1.5 s.
4. Defining the region of rejection. In order to know when we have to reject the null hypothesis (i.e. is less than m) we have to define the rejection region by specifying the critical value of z. The rejection region depends on the level of significance. The critical z value is that particular value on the x-axis of the distribution function for which the area under the distribution function to its right is exactly a percent. We can find this value from a z table: z_{x} = z(0.95) =1.645; or you may start the Teach/Me distribution calculator to calculate the value of interest.
5. Finally, we have to select the appropriate hypothesis by inserting
the numerical values for ,
µ, s and n into the equation for z. We
do not reject the null hypothesis (note the subtle difference to "we accept
the null hypothesis") if the calculated z value is smaller than z_{x}
= 1.645.
Note: A more general approach is to use the t-distribution for testing,
since the t-distribution approaches the normal distribution for large sample
sizes.
Last Update: 2005-Jul-16