July 12, 2012- Confidence Intervals for Mean (σ is known or n is < 30)

      Last Thursday, our teacher discuss briefly when to use z_a/2 or  t_a/2 values when finding the confidence intervals for the mean. She said that just remember this:


      * When the σ is known, z_a/2 no matter what the sample size is, as long as the variable is normally distributed or n ≥ 30.
      * When σ is unknown and n  ≥ 30, s can be used in the formula and z_a/2 values can be used.
      * When σ is unknown and n< 30, s is used in the formula and t_a/2 values are used, as long as the variable is approximately normally distributed.


      * Example for finding the degree of freedom:
         (Degree of freedom are the numbers that are free to vary after a sample statistics has been computed, and they tell the researcher which specific curve to use when a distribution consists of a family of curves.)
  
-Find the t_a/2 value for 90% confidence interval when the sample size is 16.
Solution: d.f = 16-1=15. find 15 in the left column and 90% in row labeled confidence intervals. The intersection where the two meets gives the value for t_a/2, which is 1.753


         *Example for finding the confidence interval of the mean where the given are mean = 0.46,d.f = 14, t_{a/2 =} 1.761, and s = 0.06.


Solution: 
       0.46 - (1.761)(o.o6/ square root of 15) < mean <  0.46 + (1.761)(o.o6/ square root of 15)
       0.46 - 0.027 < mean < 0.46 + 0.27
       0.43 < mean < 0.49


Trough the examples that our teacher gave, we have very well understand the concept about finding the confidence interval for the mean (σ is known or n is < 30).


By: Dustin Joshua Esquia
       III-Gold