Questions: Match each P-value with the graph that displays its area without performing any calculations. P=0.0089 and P=0.1977. Graph displays the area for P=0.0089 and graph displays the area for P=0.1977 because the P-value the

Match each P-value with the graph that displays its area without performing any calculations. P=0.0089 and P=0.1977.

Graph displays the area for P=0.0089 and graph displays the area for P=0.1977 because the P-value the

Transcript text: Match each P -value with the graph that displays its area without performing any calculations. Explain your reasoning. $\mathrm{P}=0.0089$ and $\mathrm{P}=0.1977$. Graph $\square$ displays the area for $\mathrm{P}=0.0089$ and graph $\square$ displays the area for $\mathrm{P}=0.1977$ because the P -value $\square$ the $\square$

Solution

Solution Steps

Step 1: Identify the P-values and corresponding graphs

The problem provides two P-values: 0.0089 and 0.1977.
We need to match these P-values with the appropriate graphs (a) and (b).

Step 2: Understand the P-value and Z-score relationship

A P-value represents the probability of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true.
The Z-score indicates how many standard deviations an element is from the mean.

Step 3: Analyze the given graphs

Graph (a) shows a Z-score of -2.37.
Graph (b) shows a Z-score of -0.85.

Step 4: Match the P-values with the graphs

A Z-score of -2.37 corresponds to a very small P-value because it is far from the mean. This matches P = 0.0089.
A Z-score of -0.85 corresponds to a larger P-value because it is closer to the mean. This matches P = 0.1977.

Final Answer

Graph (a) displays the area for P = 0.0089 and graph (b) displays the area for P = 0.1977 because the P-value is smaller for a Z-score further from the mean.

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