Test of hypothesis about the difference among two means, Mathematics

Test of hypothesis about the difference among two means

The t test can be utilized under two assumptions when testing hypothesis about the difference among the two means; that the two are normally distributed as or near normally distributed populations and that the standard deviation of the two is the similar or at any rate not significantly different.

 

Appropriate test statistic to be utilized is

      t     = (x¯1 - x¯2)/S(x¯1 - x¯2)           at (n1 + n2 - 2) d.f.

The standard deviation is acquired by pooling the two sample standard deviation as given below likes:

Sp =802_Test of hypothesis about the difference among two means.png

 

 

 

 

Whereas S1 and S2 are standard deviation for sample 1 & 2 respectively

Now Sx¯1 = Sp/√n1   and Sx¯2=  Sp/√n2  

 S(x¯1 - x¯2)=  √{ S2x¯1 + S2x¯2 }

Alternatively S(x¯1 - x¯2)=  Sp √{(n1 + n2)/n1n2}

Illustration

Two different types of drugs A and B were tried on specific patients for increasing weights, 5 persons were provided drug A and 7 persons were provided drug B. the increase in weight in pounds is described below as:

 

Drug A

8

12

16

9

3

 

 

Drug B

10

8

12

15

6

8

11

Do the two drugs differ significantly along with regard to their effect in increasing weight? As described that v= 10; t0.05 = 2.23

Solution

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

t =  (x¯1 - x¯2)/S(x¯1 - x¯2)

Calculate for x¯1 , x¯2  and S

                              2172_Test of hypothesis about the difference among two means 1.png

X1 = åx1/n1  = 45/5 = 9 ; X2 = åx2/n2 = 70/7 = 10 ;

S1 = √(62/4) = 3.94 ;  S2 = √(54/6) = 3;

Sp = {((4 * 15.4) + (6 * 9))/10}

= 3.406

S(x¯1 - x¯2) = √{(11.6/5) + (11.6/7)}

= 1.99

t = (x¯1 - x¯2)/S(x¯1 - x¯2)

 = ¦{(9 - 10)/1.99}¦

= 0.50

Now t0.05 (at v = 10) = 2.23 > 0.5

Thus we accept the null hypothesis.

Hence there is no significant difference in the efficacy of the two drugs in the matter of increasing weight

Posted Date: 2/19/2013 1:48:57 AM | Location : United States







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

Write discussion on Test of hypothesis about the difference among two means
Your posts are moderated
Related Questions
how can you tell qhich trangle is sss,asa, sas, and aas s

definition and examples and types

Write down a game each to teach children i) multiplication, ii) what a circle is, iii) estimation skills. Also say what you expect the child to know before you try to t


We know that 2 4 = 16 and also that 2 is referred to as the base, 4 as the index or power or the exponent. The same if expressed in terms of logarithms would be log 2

What is Deductive Reasoning ? Geometry is based on a deductive structure -- a system of thought in which conclusions are justified by means of previously assumed or proved sta

how do you add 1,ooo and 100?

Approximating Definite Integrals - Integration Techniques In this section we have spent quite a bit of time on computing the values of integrals. Though, not all integrals can


Classifying critical points : Let's classify critical points as relative maximums, relative minimums or neither minimums or maximums. Fermat's Theorem told us that all relative