Suppose α = 0.025. If P-value must be < 0.025 in order to reject H0, how...

Suppose α = 0.025. If P-value must be < 0.025 in order to reject H0, how many standard deviations below 0.10, must be?

Expert Solution

It depends on whether the hypothesis test being conducted is one tailed or two tailed.

Let's suppose that the test is left tailed. We also assume that the population standard deviation is known and that the sample size is large enough to compute z-statistic.

The corresponding left tailed critical z-value when p = 0.025 is:

z_c = -1.96

So in this case the test statistic must be atleast 1.96 standard deviations below the mean in order for us to reject the null hypothesis.

Next, let's suppose that the test is two tailed. Again we assume that the population standard deviation is known and that the sample size is large enough to compute z-statistic.

The corresponding left tailed critical z-value when p = 0.025 is:

z_c = -2.24

So in this case the test statistic must be atleast 2.24 standard deviations below the mean in order for us to reject the null hypothesis.

orchestra answered 2 years ago

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