A research study claims that 68% of adults drink regularly. Edward conducts a random sample of 200 people and finds that 140 people drink regularly.

**Using the formula and data provided, what is the value of the z-test statistic (answer choices are rounded to the hundredths place)?**

A.)

0.41

B.)

0.59

C.)

0.39

D.)

0.61

To solve this problem, we can perform a **z-test for a population proportion**. The formula for the z-test statistic is:

\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}
\]

Where:
- \(\hat{p}\) is the sample proportion.
- \(p\) is the population proportion.
- \(n\) is the sample size.

### Step-by-step solution:

1. **Given values:**
   - \( p = 0.68 \) (population proportion)
   - \( n = 200 \) (sample size)
   - \( \hat{p} = \frac{140}{200} = 0.70 \) (sample proportion)

2. **Calculate the standard error (SE):**

\[
SE = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.68 \times (1 - 0.68)}{200}} = \sqrt{\frac{0.68 \times 0.32}{200}} = \sqrt{\frac{0.2176}{200}} = \sqrt{0.001088} = 0.03299
\]

3. **Calculate the z-test statistic:**

\[
z = \frac{0.70 - 0.68}{0.03299} = \frac{0.02}{0.03299} \approx 0.61
\]

### Answer:
The value of the z-test statistic is approximately **0.61**, so the correct answer is **D.) 0.61**.

Would you like more details on this process or how hypothesis testing works?

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### Related questions:
1. What is the significance of the z-test statistic in hypothesis testing?
2. How would the z-test statistic change if the sample size were larger?
3. Can you explain how to interpret the results of a z-test for proportions?
4. What is the difference between a z-test and a t-test?
5. What assumptions must be met for the z-test for a population proportion to be valid?

### Tip:
In hypothesis testing, always check whether your sample size is large enough to approximate the sampling distribution as normal, especially when using the z-test for proportions.

A research study claims that 68% of adults drink regularly. Edward conducts a random sample of 200 people and finds that 140 people drink regularly. Using the formula and data provided, what is the value of the z-test statistic (answer choices are rounded to the hundredths place)?

Explore how to solve a hypothesis testing problem using a z-test for population proportions. In this example, 68% of adults drink regularly, and a sample of 200 people shows 140 regular drinkers. Learn how to calculate the z-test statistic and understand the key steps in hypothesis testing.

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