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Identify Z-Value

 Need assistance with identifying ‘Z- critical value’. I cannot determine how the -2.33 was derived from the 1% sig level on this question. Even when looking at the one tailed test Z table. I am sure I am missing something basic here. Thanks for any help,. question and answer below.

An analyst is testing to see if the mean of a population is less than 133. A random sample of 50 observations had a mean of 130. Assume a standard deviation of 5. The test is to be made at the 1% level of significance. The analyst should:



fail to reject the null hypothesis.



accept the null hypothesis.



reject the null hypothesis.


The null hypothesis is that the mean is greater than or equal to 133.

The test statistic = (sample mean - hypothesized mean) / ((sample standard deviation / (sample size)1/2)) = (130 - 133) / (5 / 501/2) = (-3) / (5 / 7.0711) = -4.24.

The critical value for a one-tailed test at a 1% level of significance is -2.33.

The calculated test statistic of -4.24 falls to the left of the critical value of -2.33, and is in the rejection region. Thus, the null hypothesis can be rejected at the 1% significance level.

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In the z-table, look up 0.01 (1% significance level). You can see that the z-score associated with this cumulative probability is -2.33.

thx for responding so quickly. looking under .01, 1% how do you know to select -2.3 as opposed to other z values. I .0104 is the value under .01 for -2.3.

You just have to figure which ones the closest. You can also take the average of the two z-scores the significance level is in between. I doubt the answer choices on the exam will be so close together that it will make a difference.

Also just so you know, if it’s a two tailed test, you would divide the significance level by two (i.e. 5% significance, look up 0.025 and 0.975).

thanks for your help.