6.1.2. Case study 2

Unit 6 - Small samples Tests (n <30)

6.1.2. Case study 2
CASE 2: Testing of difference between two means (population variances assumed equal)
Let x and s1 be the mean and standard deviation of a sample of size n1 from a normal population with mean µ1 and let y and s2 be the mean and standard deviation of another sample of size n2 from a normal population with mean µ2. To test whether the population means differ significantly, the following null hypothesis is set up:

c
(iii) Statistical decision
If t > the table value of t at the specified level of significance, reject the null hypothesis at the level, otherwise accept it.

Example 2 : Weight was recorded separately for male and female of one year old fish of species A. The mean weights of males and females are:

 

Sex

Sample size

Mean weight (g)

Variance

Male

9

70

25

Female

11

61

16


Test whether there is significant difference in mean weight of male and female fish.

Answer : Let µ1 and µ2 denote the population means of male and female fishes respectively.
e
(iii) Statistical decision
The table value of t with 18 degrees of freedom is 2.101 at 5% and 2.878 at 1% level of significance. Since tr > the table values of t at 5% and 1% level of significance, Ho is rejected i.e., there is significant difference between the mean weights of males and females.

Last modified: Monday, 12 September 2011, 10:40 AM