Site pages
Current course
Participants
General
18 February - 24 February
25 February - 3 March
4 March - 10 March
11 March - 17 March
18 March - 24 March
25 March - 31 March
1 April - 7 April
8 April - 14 April
15 April - 21 April
22 April - 28 April
6.1.2. Case study 2
Unit 6 - Small samples Tests (n <30)
6.1.2. Case study 2CASE 2: Testing of difference between two means (population variances assumed equal)
Let and s1 be the mean and standard deviation of a sample of size n1 from a normal population with mean µ1 and let 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:
(iii) Statistical decision
If > 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.
(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 > 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