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Large Sample Test for Mean
A random sample of size n (n > 30) has a sample mean . To test the hypothesis that the population mean μ has a specified value μ0 let us formulate the Null Hypothesis as H0: μ = μ0 .
The Alternative Hypothesis is (i) H1: μ ≠ μ0 or (ii) H1: μ > μ0 or (iii) H1: μ < μ0 . Since n is large, the sampling distribution of is approximately normal.
If H0 is true, the test statistic z = has approximately a standard normal distribution. The critical region for z depending on the nature of H1 and level of significance α is given below:
Level of significance ( α )
10%
5%
1%
Critical region for μ ≠ μ0
| z | > 1.64
| z | > 1.96
| z | > 2.58
Critical region for μ > μ0
z < -1.28
z < -1.64
z < -2.33
Critical region for μ < μ0
z > 1.28
z > 1.64
z > 2.33
Classification of Universe The universe may be classified either on the basis of number of units and on the basis of existence of units as is clear from the following chart :
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