According to a poll, 11.55% of adults in a certain country have diabetes. Suppose a researcher wonders if the diabetes rate in her area is higher than the national rate. She surveys 122 adults in her area and finds that 18 of them have diabetes. Complete parts a and b below. z = ± 1.1073 p = 0.2682 z = 1.1073 p=0.8659 B. If 11.55% of the adults in this area have diabetes, then there is a - 1.1073 or greater than 1.1073. Interpret the p-value. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.) A. There is a chance that more than 18 out of 122 people in this area have diabetes. C. If 11.55% of the adults in this area have diabetes, then there is a 1.1073 or less. z = 1.1073 D. If 11.55% of adults in this area have diabetes, then there is a greater. p = 0.1341 % chance of observing a z-score less than % chance of observing a z-score of % chance of observing a z-score of 1.1073 or

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**Context:**

According to a poll, 11.55% of adults in a certain country have diabetes. A researcher wonders if the diabetes rate in her area is higher than the national rate. She surveys 122 adults in her area and finds that 18 of them have diabetes. Complete parts a and b below.

**Graphs and Explanation:**

1. **Graph with z = ± 1.1073, p = 0.2682:**
   - This normal distribution curve shows a two-tailed test with z-scores of ± 1.1073. The shaded areas represent the probability in both tails, corresponding to a p-value of 0.2682.

2. **Graph with z = 1.1073, p = 0.8659:**
   - This graph illustrates a one-tailed test in the upper tail. The z-score is 1.1073, and the p-value for the shaded area on the right is 0.8659, indicating the probability of observing a z-score above 1.1073.

3. **Graph with z = 1.1073, p = 0.1341:**
   - This graph is another one-tailed test, but it focuses on the lower tail. The shaded area to the right of the z-score of 1.1073 corresponds to a p-value of 0.1341, indicating the probability of observing a z-score of 1.1073 or less.

**Question:**

Interpret the p-value. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.)

**Options:**

A. There is a __% chance that more than 18 out of 122 people in this area have diabetes.

B. If 11.55% of the adults in this area have diabetes, then there is a __% chance of observing a z-score less than -1.1073 or greater than 1.1073.

C. If 11.55% of the adults in this area have diabetes, then there is a __% chance of observing a z-score of 1.1073 or less.

D. If 11.55% of adults in this area have diabetes, then there is a __% chance of observing a z-score of 1.1073 or greater.
Transcribed Image Text:**Context:** According to a poll, 11.55% of adults in a certain country have diabetes. A researcher wonders if the diabetes rate in her area is higher than the national rate. She surveys 122 adults in her area and finds that 18 of them have diabetes. Complete parts a and b below. **Graphs and Explanation:** 1. **Graph with z = ± 1.1073, p = 0.2682:** - This normal distribution curve shows a two-tailed test with z-scores of ± 1.1073. The shaded areas represent the probability in both tails, corresponding to a p-value of 0.2682. 2. **Graph with z = 1.1073, p = 0.8659:** - This graph illustrates a one-tailed test in the upper tail. The z-score is 1.1073, and the p-value for the shaded area on the right is 0.8659, indicating the probability of observing a z-score above 1.1073. 3. **Graph with z = 1.1073, p = 0.1341:** - This graph is another one-tailed test, but it focuses on the lower tail. The shaded area to the right of the z-score of 1.1073 corresponds to a p-value of 0.1341, indicating the probability of observing a z-score of 1.1073 or less. **Question:** Interpret the p-value. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.) **Options:** A. There is a __% chance that more than 18 out of 122 people in this area have diabetes. B. If 11.55% of the adults in this area have diabetes, then there is a __% chance of observing a z-score less than -1.1073 or greater than 1.1073. C. If 11.55% of the adults in this area have diabetes, then there is a __% chance of observing a z-score of 1.1073 or less. D. If 11.55% of adults in this area have diabetes, then there is a __% chance of observing a z-score of 1.1073 or greater.
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