What is the test statistic? p - P (P1 – P2) – (P1 – P2) (ž1 – 72) - (41 – 42) (71 – 2) - (41 – 42) (n – 1)² . s² Ox O F Ota (71 – #2) – (141 – 42) Ot = + of ||

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**What is the test statistic?**

- \( z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \)

- \( z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{p \cdot q}{n_1} + \frac{p \cdot q}{n_2}}} \)

- \( z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \)

- \( t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \)

- \( \chi^2 = \frac{(n - 1) s^2}{\sigma^2} \)

- \( F = \frac{s_1^2}{s_2^2} \)

- \( t_d = \frac{\bar{x} - \mu_d}{\frac{s_d}{\sqrt{n}}} \)

- \( t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \)

- \( z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \)
Transcribed Image Text:**What is the test statistic?** - \( z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \) - \( z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{p \cdot q}{n_1} + \frac{p \cdot q}{n_2}}} \) - \( z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \) - \( t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \) - \( \chi^2 = \frac{(n - 1) s^2}{\sigma^2} \) - \( F = \frac{s_1^2}{s_2^2} \) - \( t_d = \frac{\bar{x} - \mu_d}{\frac{s_d}{\sqrt{n}}} \) - \( t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \) - \( z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \)
### Investigation of Childcare Responsibility Among Fathers

**Context:**
An article in a journal reports that 34% of American fathers take no responsibility for childcare. A researcher claims that this figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton revealed that 96 did not help with childcare.

**Questions for Analysis:**

1. **How many populations?**
   - Options:
     - 1
     - 2

2. **What is the parameter?**
   - Options:
     - Mean
     - Proportion
     - Difference between Means
     - Variance
     - Standard Deviation

The focus of this study is to determine whether the proportion of fathers in Littleton who do not participate in childcare responsibilities is significantly higher compared to the reported national figure. The analysis will involve comparing proportions between two populations: American fathers overall and fathers in Littleton.
Transcribed Image Text:### Investigation of Childcare Responsibility Among Fathers **Context:** An article in a journal reports that 34% of American fathers take no responsibility for childcare. A researcher claims that this figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton revealed that 96 did not help with childcare. **Questions for Analysis:** 1. **How many populations?** - Options: - 1 - 2 2. **What is the parameter?** - Options: - Mean - Proportion - Difference between Means - Variance - Standard Deviation The focus of this study is to determine whether the proportion of fathers in Littleton who do not participate in childcare responsibilities is significantly higher compared to the reported national figure. The analysis will involve comparing proportions between two populations: American fathers overall and fathers in Littleton.
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