A recent study shows that 17 % of a random sample of 1954 cell phone owners do most of their online browsing on their phone. The standard error for the proportion is 0.0085. The sample size is large enough to use a normal distribution. 1Smith, A., "Cell Internet Use 2012;" Pew Research Center, pewresearch.org, June 26, 2012.

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### Statistical Analysis Instructions

#### (c) Test Statistic and \( p \)-Value Calculation

**Instructions:**

1. **Calculate the Test Statistic and \( p \)-Value:**
   - Provide the test statistic and the \( p \)-value.
   - Round the test statistic to two decimal places.
   - Round the \( p \)-value to three decimal places.

2. **State the Conclusion:**
   - Based on the test statistic and \( p \)-value, draw a conclusion about the null hypothesis \( H_0 \).

**Input Fields:**

- **Test Statistic:**
  - Enter the computed test statistic.
  - The input box for the test statistic looks as follows:
    \[
    \text{Test statistic} = \square
    \]

- **\( p \)-Value:**
  - Enter the computed \( p \)-value.
  - The input box for the \( p \)-value looks as follows:
    \[
    p\text{-value} = \square
    \]

- **Conclusion Dropdown:**
  - Use the dropdown menu to select the appropriate conclusion concerning the null hypothesis \( H_0 \).
  - The conclusion section is represented as follows:
    \[
    \text{Conclusion: } \boxed{\square} \quad H_0 
    \]

Ensure your answers follow the given rounding conventions and select the appropriate conclusion based on your statistical results.
Transcribed Image Text:### Statistical Analysis Instructions #### (c) Test Statistic and \( p \)-Value Calculation **Instructions:** 1. **Calculate the Test Statistic and \( p \)-Value:** - Provide the test statistic and the \( p \)-value. - Round the test statistic to two decimal places. - Round the \( p \)-value to three decimal places. 2. **State the Conclusion:** - Based on the test statistic and \( p \)-value, draw a conclusion about the null hypothesis \( H_0 \). **Input Fields:** - **Test Statistic:** - Enter the computed test statistic. - The input box for the test statistic looks as follows: \[ \text{Test statistic} = \square \] - **\( p \)-Value:** - Enter the computed \( p \)-value. - The input box for the \( p \)-value looks as follows: \[ p\text{-value} = \square \] - **Conclusion Dropdown:** - Use the dropdown menu to select the appropriate conclusion concerning the null hypothesis \( H_0 \). - The conclusion section is represented as follows: \[ \text{Conclusion: } \boxed{\square} \quad H_0 \] Ensure your answers follow the given rounding conventions and select the appropriate conclusion based on your statistical results.
### Study Analysis

A recent study<sup>1</sup> shows that 17% of a random sample of 1954 cell phone owners do most of their online browsing on their phone. The standard error for the proportion is 0.0085. The sample size is large enough to use a normal distribution.

---

#### Reference:
<sup>1</sup>Smith, A., “Cell Internet Use 2012,” Pew Research Center, pewresearch.org, June 26, 2012.

---

#### Statistical Analysis:
(a) **Confidence Interval Calculation**

Find a 95% confidence interval for the proportion of cell phone owners who do most of their online browsing on their phone.

*Round your answers to one decimal place.*

\[ \text{The 95% confidence interval is } [ \mathbf{} \% \mathrm{ \ to \ } \mathbf{} \% . ] \]

---

(b) **Hypothesis Testing**

Use a normal distribution to test whether there is evidence that the proportion is greater than 0.15.

*State the null and alternative hypotheses.*

\[ H_0: p \leq 0.15 \]
\[ H_a: p > 0.15 \]

---

Use the given standard error and confidence level to complete these calculations.
Transcribed Image Text:### Study Analysis A recent study<sup>1</sup> shows that 17% of a random sample of 1954 cell phone owners do most of their online browsing on their phone. The standard error for the proportion is 0.0085. The sample size is large enough to use a normal distribution. --- #### Reference: <sup>1</sup>Smith, A., “Cell Internet Use 2012,” Pew Research Center, pewresearch.org, June 26, 2012. --- #### Statistical Analysis: (a) **Confidence Interval Calculation** Find a 95% confidence interval for the proportion of cell phone owners who do most of their online browsing on their phone. *Round your answers to one decimal place.* \[ \text{The 95% confidence interval is } [ \mathbf{} \% \mathrm{ \ to \ } \mathbf{} \% . ] \] --- (b) **Hypothesis Testing** Use a normal distribution to test whether there is evidence that the proportion is greater than 0.15. *State the null and alternative hypotheses.* \[ H_0: p \leq 0.15 \] \[ H_a: p > 0.15 \] --- Use the given standard error and confidence level to complete these calculations.
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