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When carrying out a large sample test of H0: µ0 = 50, Ha: µ0 < 50,...

When carrying out a large sample test of H0: µ0 = 50, Ha: µ0 < 50, we reject H0 at level of significance α when the calculated test statistic is:

Greater than zα

Less than zα

Greater than zα/2

Less than – zα
Math   Statistics-And-Probability   
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Answer #1

Here the test is an one tailed test, i.e. a left tailed test... So under Ho the test statistic follows a standard normal distribution. Since it is a left tailed test, the critical region will be at the left side of the null hypothetical distribution curve and at level of significance we reject H0 if the value of the test statistic under H0 is less than -z. So the 4th option is correct. The picture of null hypothetical and alternative hypothetical distribution curve and the critical region is shown below for better understanding.

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