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
Explain English System in details? There are three types of measurements that can be taken using the English System: length, distance, weight, and capacity. Length and dista

Initial Conditions and Boundary Conditions In many problems on integration, an initial condition (y = y 0 when x = 0) or a boundary condition (y = y

How tall does a cone with diameter of 10 inches have to be to fit exactly half of a sphere with a diameter of 10 inches inside it?

How do you compute the phase/angle of a complex number? i.e 1+2i

how do i know what operation to use in a fraction word problem

Let a and b be fixed real numbers such that a The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all r

1a.if the williams spend $385 a month on food what is their monthly income

solve for y given that 3sin^2 y+cos y-1=0 for 0y360

If i worked 7 1/3 hours and planted 11 trees how many hours did it take to plant each tree?

Solve the following equestions i.2x-8=8 ii.3x+2/5=4 iii.8/3x-2=2 iv.0.6x-5=7