Postpartum depression and anxiety (PPD), is a common medical condition affecting mothers and their families after the birth of a baby. The CDC estimated that 12%12% of women who have recently given birth suffer from PPD. However, this research only reflected self-reported cases. Therefore, one group dedicated to helping women and their families with PPD believes that the true percentage of women who suffer from PPD is much higher. The group conducts a simple random sample of 143143 women who had given birth in the last year and discovers that 2525 of them report having PPD. Based on this evidence, can the group claim that the true percentage of women who have PPD is greater than 12%12%? Use a 0.010.01 level of significance.

Step 2 of 3 :  

Compute the value of the test statistic. Round your answer to two decimal places.

To compute the value of the test statistic, follow these steps:

### Step 1: Define the hypotheses

- **Null Hypothesis (H₀):** \( p = 0.12 \) (The true percentage of women who have PPD is 12%.)
- **Alternative Hypothesis (H₁):** \( p > 0.12 \) (The true percentage of women who have PPD is greater than 12%.)

### Step 2: Compute the sample proportion

The sample proportion \( \hat{p} \) is calculated as:

\[
\hat{p} = \frac{\text{Number of women reporting PPD}}{\text{Total number of women in the sample}} = \frac{25}{143}
\]

\[
\hat{p} = 0.1748
\]

### Step 3: Compute the standard error

The standard error \( SE \) is given by:

\[
SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12(1-0.12)}{143}}
\]

\[
SE = \sqrt{\frac{0.12 \times 0.88}{143}} = \sqrt{\frac{0.1056}{143}} \approx \sqrt{0.000738} \approx 0.0272
\]

### Step 4: Compute the test statistic

The test statistic \( z \) is computed using the formula:

\[
z = \frac{\hat{p} - p}{SE} = \frac{0.1748 - 0.12}{0.0272} \approx \frac{0.0548}{0.0272} \approx 2.01
\]

Thus, the value of the test statistic is approximately **2.01**.

Would you like more details on how to proceed with this hypothesis test, or have any other questions?

Here are five related questions you might consider:
1. How do you interpret the p-value associated with this test statistic?
2. What are the steps to determine if the null hypothesis should be rejected?
3. What role does the level of significance (0.01) play in this test?
4. How does increasing the sample size affect the reliability of the test?
5. How might the group address potential biases in self-reported data?

**Tip:** When performing hypothesis tests, it’s essential to ensure the assumptions of the test (such as random sampling and a sufficiently large sample size) are met to obtain valid results.

Learn how to conduct hypothesis testing to determine if the true percentage of women suffering from postpartum depression and anxiety (PPD) is greater than 12%. This problem involves computing sample proportions, standard errors, and test statistics with a 0.01 level of significance. Explore detailed steps and interpretations.

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