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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 )
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
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