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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