Statistical Inference

9. STATISTICAL INFERENCE

    

    Today is May 6, 2011 (Friday). Without much a do please welcome our reporter Ma’am Agustin.

    Our session started with prayer.

    Ready begin…

    An estimate of a population parameter given by a single number is called a point of estimate of the parameter. An estimate of populations parameter may be considered to lie is called interval estimate of the parameter.

CONFIDENCE INTERVALS FOR MEANS

    The percentage confidence is often called the confidence level. The numbers in the confidence limits is called confidence or coefficients critical values and are denoted by z.

1. Large sample (n>30)

If the statistic is the sample mean X, then the confidence interval is

                X + z_c  

                                

                                 n

If sampling is without replacement from a population of finite size N, then the confidence interval for the population mean is

       

Example:

Find a 95% confidence interval for a population mean     for

    N=36,  x = 15.2,  s²=2.56  or  s = 1.6

Solution:

     Since the sample size of n=36 is large, the distribution of the sample mean   x is approximately normally distributed with mean  and standard error        . The approximate 95% confidence interval is

2. Small samples (n< 30)

In this case the t distribution to obtain the confidence level

CONFIDENCE INTERVALS FOR PROPORTIONS

     The confidence limits for the population proportion are given by

            

In case sampling is from an infinite population or if sampling is with replacement from a finite population.

If sampling is without replacement from a population of finite size N, the confidence limits are.

Example:

1. A random sample of n = 400 observations from a binomial population produced x = 248 successes. Find a 95% confidence interval for p.

Solution:

    The point estimate for p is

       P = x = 248   = 0.62

                    n     400

And the standard error is

CONFIDENCE INTERVALS FOR DIFFERENCES

     The confidence limits for the difference of two population means, where the populations are infinite, are given by,

    

Similarly confidence limits for the difference of two population proportions, where the populations are infinite. Are given by;

P1 – P2  zcP1 – P2   =  P1 – P2  z         P1 – (1- P1)   + P2 – (1- P2) 

                                                                                    n1                   n2  

Oh quarter of ten already, I felt hungry.

Wow very nice the reporter serves snacks. Thank you Ma’am Agustin.

Though a little, but at least I learned today.

Reference;

Statistics for Filipino Students- by Ma. Carmelita A. Batacan