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)

Illustration

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?

Solution

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

Evaluate the subsequent integral. Solution This is an innocent enough looking integral. Though, because infinity is not a real number we cannot just integrate as norm

How do you find the area of a circle given the diameter?

A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"

Give the Proofs in Mathematics ? 1 Two-column deductive proof Proof: Statements                                                              Reasons * Start with given c

i just have one question i need help on for my geometry homework

a part of a line with two end points.

1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase

how to work out consumer arithmetic?

Q1- different types of rectilinear figures? Q2- interior and exterior angles of the polygon? Q3-relation between interior and exterior angles of polygons? Q4- properties of any fiv