Discussion
For testing of hypothesis \(H_{0} : M_{1} = M_{2}\) and \(H_{1} : M_{1} \lt M_{2}\), the critical value of Z at 5% level of significance when size of sample is more than 30 is
Answer: C
The test is a one tailed test, since the alternative hypothesis is that the first mean is less than the second, and the critical value of Z at the 5 per cent level of significance for a large sample is 1.645, option C. In a one tailed test the whole 5 per cent is placed in one tail of the normal distribution. The value 1.96 is the critical value for a two tailed test at 5 per cent. The value 2.32 is the one tailed value at 1 per cent, and 2.5758 is the two tailed value at 1 per cent.
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