When the significance of difference is to be tested between population mean and sample mean or between two sample means either test or test is applied as given below:
T-Test: It is used when the sample size is large.
Z-Test: It is used when the sample size is small. It is of two types as given below:
Student's: It is used when the observations are paired.
Fisher's It is used when the observations are not paired.
For practical purposes, sample may be regarded as large if it is more than 30 and small if it is less than or equal to 30. The calculated value of z or is compared with their table value at appropriate degrees of freedom. If the calculated value is greater than table value, it is considered as significant and vice versa.
When a random sample is drawn from a population, it is expected that it will be a true representative of the population and should not differ significantly from the base population, accepting null hypothesis. If the sample mean differs significantly from population mean, it rejects the null hypothesis and suggests that the sample mean is not a true representative of the population. In plant breeding, significance of z test or test between the selected plant sample and base population indicates effectiveness of selection.
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