Consider the two independent random samples:
- Set up H0 : σ21 = σ22
- Set up H1 : σ21< σ22 or σ21> σ22, or σ21 ≠ σ22
- Statistics to set up level of significance:
Statistics and Operational Research:
Here, F-distribution will be followed depending on H1, critical value. We have discussed it in the tablebelow:
| H1 | Test Statistics | Reject H0, if |
| σ21< σ22 | F = | Fcal>Fα,n2 -1, n1 – 1 |
| σ21> σ22 | F = | Fcal>Fα,n1 -1, n2 – 1 |
| σ21≠ σ22 | F = | Fcal>Fα/ 2,nL -1, nl – 1 |
Example No. 13:
Test the null hypothesis of the following if the intensity of light of two bulbs manufactured by two companies A and B respectively has yield of S1 = 1.5 foot-candles, S2 = 1.75 foot-candles from a sample size of 16. Here, σ12 = σ22for alternative σ12<σ22 at the level of significance as 0.01.
Solution:
- Set up H0 : σ12 = σ22
- Set up H1 : σ12<σ22
- Statisticswhich follows the F-Distribution with degree of freedom as 15 and 15
- α = 0.01. here, alternative hypothesis shows, it is left tailed test.
Thus,
Critical Value, F0.01, 15, 15 = 3.52
- Given:
S1 = 1.5 foot-candles
S2 = 1.75 foot-candles
- Decision:
Fcal< 3.52
Hence,
H0 is accepted and there will be no variability in intensity of light by these two bulbs.
Links of Previous Main Topic:-
- Introduction to statistics
- Knowledge of central tendency or location
- Definition of dispersion
- Moments
- Bivariate distribution
- Theorem of total probability addition theorem
- Random variable
- Binomial distribution
- What is sampling
- Estimation
- Statistical hypothesis and related terms
- Test for large samples n 30
- Testing of small samples
- Testing of proportion
- Testing of single variance
Links of Next Statistics Topics:-
- Analysis of variance introduction
- Definition of stochastic process
- Introduction operations research
- Introduction and mathematical formulation in transportation problems
- Introduction and mathematical formulation
- Queuing theory introduction
- Inventory control introduction
- Simulation introduction
- Time calculations in network
- Introduction of game theory
