assume the normal distribution applies to a scenario where you are given h1 p<0.08 in a test using a significance level of a=0.01. Find the critical z value(s)

Answer is z=-2.33

Why? Can you explain it (step by step) I'd like to understand
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1 Answer

In this problem we’re looking at an inequality. Less than means we are looking at the left side of the normal distribution, rather than looking at both sides of the distribution and considering an interval on either side of the mean. All the Z values to the left of the mean (that is, less than the mean) have negative values. The significance level tells us how far over to the left. We are considering the left tail of the distribution, so 99% of the distribution lies to the right of this tail. Tables usually give the percentage to the left of the Z value. Therefore, if the confidence level is 99% (significance level is 1%, ɑ=0.01), the Z value is about 2.33, meaning 99% of the distribution is 2.33 standard deviations above the mean. By symmetry the left tail and the right tail each represent 1% of the distribution. We need the left tail, so the Z value we need is 2.33 standard deviations below the mean, represented by Z=-2.33.

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