Question

Emile has calculated a one-tailed z-statistic of -1.97 and wants to see if it is significant at the 5% significance level.

Answer 1

Answer:

Z = -1.65

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the critical value for the 5% significance level?

One-tailed statistic, so Z with a p-value of 0.05.

Looking at the z-table, this is Z = -1.65, so this is the critical value for the 5% significance leve.