Question

Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P = 0.0158 and P=0.1762.

(a) = -2.15
(b) z= -0.93
Graph
displays the area for P=0.0158 and graph
displays the area for P = 0.1762 because the P-value
Click to select your answer(s) and then click Check Answer

Answer 1

The graph for P=0.0158 matches with a z-score of -2.15 since smaller P-values represent more extreme z-scores, while the graph for P=0.1762 corresponds with a z-score of -0.93, as larger P-values indicate z-scores closer to the mean.

Step-by-step explanation:

Matching each P-value with the graph that displays its area involves understanding the relationship between P-values and z-scores. A P-value represents the area under the standard normal distribution curve to the left of a given z-score. The smaller the P-value, the further to the tail end of the curve (and thus a more extreme z-score) it corresponds to, while a larger P-value indicates a z-score closer to the mean.

The P-value 0.0158, is a relatively small number, suggesting that it corresponds to a z-score that is more extreme, meaning further into the tail of the normal distribution. Accordingly, graph (a), which corresponds to z = -2.15, would be the graph that displays the area for P=0.0158 since z-scores with larger absolute values are associated with smaller P-values.

In contrast, a P-value of 0.1762 is larger, indicating that the associated z-score is closer to the mean of the distribution. Therefore, graph (b), with z = -0.93, would represent the P-value of 0.1762 since z-scores closer to zero reflect larger P-values.

Answer 2

a) z = -2.15 has p-value = 0.0158

b) z = -0.93 has p value = 0.1762

Step-by-step explanation:

We are given two z-scores and two p-values and we have to identify which p-value belongs to which z-score without using any calculator/table.

To solve this problem we need to understand about the p-value of the z-score and what does it represent. The p-value of a z-score represents the area under the graph in a standard normal curve which is to the left of that z-score. If the z-score is increased, the area to its left will increase, so this means the p-value will also increase.

From the given z-scores, z = - 2.15 is smaller than z = - 0.93. This means the area to the left of z = - 2.15 in a standard normal curve will be lesser than that of z = - 0.93. Hence, the p-value for z = - 2.15 will be lesser than the p-value of z = - 0.93

So,

p-value for z = - 2.15 is p = 0.058

and

p-value for z = 0.1762 is p = 0.1762