Small samples-estimation of population mean , Mathematics

Estimation of population mean

If the sample size is small (n<30) the arithmetic mean of small samples are not normally distributed. In such conditions, student's t distribution must be utilized to estimate the population mean.

In this case

Population mean µ = x¯ ±  tS

 x¯ = Sample mean

S =  s/√n

S = standard deviation of samples = 1985_Estimation of population mean.png

for small samples.

n = sample size

v = n - 1 degrees of freedom.

The value of t is acquired from student's t distribution tables for the essential confidence level


A random sample of 12 items is taken and is found to have a mean weight of 50 gram and a standard deviation of 9 gram

What is the mean weight of population

a)         Along with 95 percent confidence

b)         Along with 99 percent confidence


   S = 9; v = n - 1 = 12 - 1 = 11;          

S= s/√n = 9/√12        

µ = x¯ ± t S 

At 95 percent confidence level

µ = 50 ± 2.262

= 50 ± 5.72 grams

Hence we can state with 95 percent confidence that the population mean is among 44.28 and 55.72 gram

At 99 percent confidence level

µ = 50 ± 3.25 (9/√12)

= 50 ± 8.07 gram

 Therefore we can state with 99 percent confidence that the population mean is between 41.93 and 58.07 grams

Note: To employ the t distribution tables it is significant to find the degrees of freedom (v = n - 1). In the illustration above v = 12 - 1 = 11

From the tables we find that at 95 percent confidence level against 11 and under 0.05, the value of t = 2.201


Posted Date: 2/19/2013 1:04:32 AM | Location : United States

Related Discussions:- Small samples-estimation of population mean , Assignment Help, Ask Question on Small samples-estimation of population mean , Get Answer, Expert's Help, Small samples-estimation of population mean Discussions

Write discussion on Small samples-estimation of population mean
Your posts are moderated
Related Questions

Let E = xy + y't + x'yz' + xy'zt', find (a)   Prime implicants of E,  (b)  Minimal sum for E.  Ans:  K -map for following boolean expression is given as: Prime implic

use an expression to write an expression with five 3s that has a value of 0

A Pythagorean triple is a set of positive integers (a,b,c) like  a2 + b2 = c2.  Write a function "ispythag" that will receive 3 positive integers (a, b, c in that order) and will r

The time has at last come to describe "nice enough". We've been using this term during the last few sections to explain those solutions which could be used to form a general soluti

Unit circle A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle.  The unit circle is very useful in Trigonometry. (b) x 2 + ( y - 3) 2

Variation of Parameters Notice there the differential equation, y′′ + q (t) y′ + r (t) y = g (t) Suppose that y 1 (t) and y 2 (t) are a fundamental set of solutions for

L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12   R.H.S =c

Describe Simplifying Fractions with example? When a fraction cannot be reduced any further, the fraction is in its simplest form. To reduce a fraction to its simplest form, div