Estimation of difference among two means, Mathematics

Estimation of difference among two means

We know that the standard error of a sample is given by the value of the standard deviation (σ) divided by the square root of the number of items in the sample (√n).

However, when given two samples, the standard errors is described by

885_Estimation of difference among two means.png

Also note that we do calculate approximately the interval not from the mean although from the difference between the two samples means that is: (x¯A - x¯B)

The appropriate number of confidence level does not change

Thus the confidence interval is described by:

 (x¯A - x¯B) ± Confidence level S(A - x¯B)

=  (x¯A - x¯B)  ± Z  S(A - x¯B)


Given two samples A and B of 100 and 400 items respectively, they contain the means x¯1= 7 ad x¯2 = 10 and standard deviations of 2 and 3 respectively. Construct confidence interval at 70 percent confidence level?


Sample                        A                                  B

                               x¯1 =      7                      x¯2= 10

                               n1 = 100                       n2 = 400

                               S1 = 2                           S2 = 3

The standard error of the samples A and B is described by:

S(A - x¯B) = √{(4/100) + (9/400)}

= ¼ = 0.25

At 70 percent confidence level, then appropriate number is equal to 1.04 or as read from the normal tables

(x¯1 - x¯2)= 7 - 10 = - 3 = 3

We take the absolute value of the difference among the means for illustration, the value of   x¯ = absolute value of X that is a positive value of X.

Therefore Confidence interval is described by:

= 3± 1.04 (0.25 )          From the normal tables a z value of 1.04 provide a value of 0.7.

= 3± 0.26

= 3.26 and 2.974

Hence 2.974 ≤ X ≤ 3.26

Posted Date: 2/19/2013 12:31:50 AM | Location : United States

Related Discussions:- Estimation of difference among two means, Assignment Help, Ask Question on Estimation of difference among two means, Get Answer, Expert's Help, Estimation of difference among two means Discussions

Write discussion on Estimation of difference among two means
Your posts are moderated
Related Questions
If sec A = x+i/x, prove that sec A + tan A = 2x or 1/2x

The Daily News reported that 54% of people surveyed said in which they would vote for Larry Salva for mayor. Based on the survey results, if 23,500 people vote in the election, how

Describe the Sample of Exponents ? Imagine, for example, that you are the P.E. coach at your school, and you need to divide one of your classes into teams. Your team has 45 stu

Find the Quadratic polynomial whose sum and product of zeros are √2 + 1, 1/ √2 + 1 Ans:    sum = 2  √2 Product = 1 Q.P = X 2 - (sum) x + Product ∴ x 2 - (2 √2 )

Now we have to start looking at more complicated exponents. In this section we are going to be evaluating rational exponents. i.e. exponents in the form

sq root of tan x dx

what is break even point and how can it helps managers to make decisions?

how do you add all the Y.AND X UP WITH 3

By selling a violin for $4950, giving a 10% discount on the marked price, a trader gained $950 on his investment, Find, Cost price.