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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
Application of the chi Square Test
Standard Error The measure of reliability of the estimating equation that we have developed is given by standard error of estimate. The standard error of estimate represented b
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