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
Complex numbers from the eigenvector and the eigenvalue. Example1 : Solve the following IVP. We first require the eigenvalues and eigenvectors for the given matrix.

Which of the subsequent numbers will yield a number larger than 23.4 while it is multiplied by 23.4? When multiplying through a number less than 1, you get a product in which i

if the ratio of boys to girls ism 3 to 5, then what percent of the students are boys

Sums and Differences of Cubes (and other odd powers)? You can factor a sum or difference of cubes using the formulas a 3 - b 3 = (a - b )(a 2 + ab + b 2 ) and a 3 + b 3 =

The logarithm of a provided number b to the base 'a' is the exponent showing the power to which the base 'a' have to be raised to get the number b. This number is defined as log a

A fish tank has the base area of 45 cm3 and is filled to the depth of 12 cm.If the height is 25 cm then how much more will be needed to fill the rest of the tank?

Convert measurements between the English system? To convert measurements between the English system and the metric system: 1. Look up the conversion between the two units of

prove That J[i] is an euclidean ring