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
Factor by grouping each of the following. 3x 2 - 2x + 12x - 8 Solution           3x 2 - 2x + 12x - 8 In this case we collect the first two terms & the final two te

( a+2b)x + (2a - b)y = 2, (a - 2b)x + (2a +b)y = 3 (Ans: 5b - 2a/10ab , a + 10b/10ab ) Ans: 2ax + 4ay = y , we get 4bx - 2by = -1 2ax+ 4ay = 5  4bx- 2by = - 1

Standardization of Variables - Before we use the general distribution curve to determine probabilities of the continuous variables, we require standardizing the original units

An investment advisory firm manages funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client's portfolio to be invested

What is the greatest common factor of 24 and 64? List the factors of 24 and 64. The largest factor that they have in common is the greatest common factor. Factors of 24: 1,

Ask question #Minimum 100 words what is the hypotunus of a right bangled triangle a=5@ b=25 find c accwhepted#

the mass of a container is 5.81kg when full with sugar .the mass of container is 3.8kg when 3/8 of the sugar is removed.what is the mass of empty container

MINIMAX regret method Minimax method assumes that the decision maker will experience 'regret' after he has made the decision and the events have happened. The decision maker ch

The m&m factory produces 2,500 packs of plain m&ms each day. Represent the total number of packs of plain m&ms the factory makes each day

Classification :  As you know, classification (also called grouping) involves putting together things that have some characteristic in common. We can say that a child is able to c