To solve the problem described in the image, we will compute the P-value for Deidre's Z-test. The Z-statistic $z = 2.11$ has already been calculated. Let's determine the correct P-value based on this Z-statistic.

Step-by-Step Solution:

1. Find the P-value for $z = 2.11$:

   The P-value is determined by finding the area under the standard normal curve beyond $z = 2.11$. Since this is a two-tailed test (based on $H_1: p_A \neq p_B$), we calculate: $P = 2 \cdot P(Z > 2.11)$

   Using a standard normal table or statistical software:

   • $P(Z > 2.11) = 1 - P(Z \leq 2.11)$
   • From the Z-table, $P(Z \leq 2.11) \approx 0.9826$
   • Thus, $P(Z > 2.11) = 1 - 0.9826 = 0.0174$

   Therefore: $P = 2 \cdot 0.0174 = 0.0348$

Final Answer:

The P-value is: $P \approx 0.0348$

Interpretation:

Since $P < \alpha = 0.05$, we reject the null hypothesis $H_0: p_A = p_B$. There is significant evidence to suggest that the defect rates differ between the two manufacturing centers.

Would you like further clarification or an explanation of how to use the Z-table?
Here are 5 related questions for practice:

1. What is the meaning of a two-tailed hypothesis test in this context?
2. How would the conclusion change if $\alpha = 0.01$?
3. How can statistical software be used to find the P-value more efficiently?
4. Why do we multiply by 2 in a two-tailed test?
5. What steps would be different if this were a one-tailed test?

Tip: Always double-check your P-value by using both Z-tables and statistical software to ensure accuracy.