Problem
State whether the standardized test statistic $z$ indicates that you should reject the null hypothesis.
(a) $z=1.889$
(b) $z=1.988$
(c) $z=-1.725$
(d) $z=-2.068$
(b) For $z=1.988$, should you reject or fail to reject the null hypothesis?
A. Fail to reject $\mathrm{H}_{0}$ because $z>1.960$.
B. Reject $\mathrm{H}_{0}$ because $\mathrm{z}>1.960$
C. Reject $\mathrm{H}_{0}$ because $-1.960
Solution
Step 1 ：Given the standardized test statistic $z=1.988$
Step 2 ：We are asked to determine whether we should reject or fail to reject the null hypothesis
Step 3 ：The null hypothesis is typically rejected if the absolute value of the z-score is greater than 1.96 (for a confidence level of 95%)
Step 4 ：This is because a z-score of 1.96 or higher (or -1.96 or lower) indicates that the observed data is very unlikely under the null hypothesis (less than 5% chance)
Step 5 ：Therefore, if the z-score is greater than 1.96 or less than -1.96, we reject the null hypothesis
Step 6 ：In this case, the z-score is 1.988, which is greater than 1.96
Step 7 ：\(\boxed{\text{Therefore, we should reject the null hypothesis}}\)
From Solvely APP
Solution
Step 1 ：Given the standardized test statistic $z=1.988$
Step 2 ：We are asked to determine whether we should reject or fail to reject the null hypothesis
Step 3 ：The null hypothesis is typically rejected if the absolute value of the z-score is greater than 1.96 (for a confidence level of 95%)
Step 4 ：This is because a z-score of 1.96 or higher (or -1.96 or lower) indicates that the observed data is very unlikely under the null hypothesis (less than 5% chance)
Step 5 ：Therefore, if the z-score is greater than 1.96 or less than -1.96, we reject the null hypothesis
Step 6 ：In this case, the z-score is 1.988, which is greater than 1.96
Step 7 ：\(\boxed{\text{Therefore, we should reject the null hypothesis}}\)
