Final answer:
The critical value at the 5% significance level for a one-tailed z-test is -1.645. Since Emile's z-statistic of -1.97 is to the left of this critical value, the result is considered statistically significant and the null hypothesis would be rejected. The correct option is B. -1.64
Step-by-step explanation:
Emile has calculated a one-tailed z-statistic of -1.97 and is interested in determining if this is significant at the 5% significance level. When looking at a normal distribution, we use the concept of a critical value to decide whether a given statistic is significant.
Specifically, for a one-tailed test, the critical z-value that corresponds to a 5% level of significance in the left tail of the distribution is -1.645. This value is significant because it represents a cutoff point; if a z-score is to the left of -1.645 (i.e., a more negative value), it is considered statistically significant at the 5% level.
In Emile's case, since -1.97 is to the left of -1.645, it means that Emile's test statistic falls within the region of rejection, and therefore, the null hypothesis would be rejected, indicating a statistically significant result at the 5% level of significance.
The correct option is B. -1.64