Final answer:
Based on the provided z values for a left-tailed test, none are smaller than the critical value of -1.645; hence, for all cases—(a) z = 1.247, (b) z = -1.337, (c) z = -1.524, and (d) z = -1.195—the null hypothesis is not rejected.
Step-by-step explanation:
The student is asking whether they should reject the null hypothesis based on the provided standardized test statistic, z, in a left-tailed test. The critical z-value is -1.645 for a significance level (α) of 0.05, which means that for values of z that are less than -1.645, we reject the null hypothesis. Here's a breakdown for each test statistic provided by the student:
- (a) z = 1.247: This value is to the right of the critical value, so we do not reject the null hypothesis.
- (b) z = -1.337: This value is to the right of the critical value (-1.645), so we also do not reject the null hypothesis.
- (c) z = -1.524: This value is closer to the critical value but still to the right, so we do not reject the null hypothesis.
- (d) z = -1.195: Again, this value is to the right of the critical value, so we do not reject the null hypothesis.
None of the provided z values are less than -1.645, so based on this information, we would not reject the null hypothesis for any of the given standardized test statistics.