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

Posted Date: 9/15/2012 3:36:51 AM | Location : United States

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