A 2018 poll of 3619 randomly selected users of a social media site found that 2463 get most of their news about world events on the site. Research done in 2013 found that only 46% of all the site users reported getting their news about world events on this site. a. Does this sample give evidence that the proportion of site users who get their world news on this site has changed since 2013? Carry out a hypothesis test and use a 0.05 significance level. b. After conducting the hypothesis test, a further question one might ask is what proportion of all of the site users get most of their news about world events on the site in 2018. Use the sample data to construct a 95% confidence interval for the population proportion. How does your confidence interval support your hypothesis test conclusion?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
icon
Related questions
Question

B please and thank you

### Educational Website Text

#### Hypothesis Testing on Social Media News Consumption

In 2018, a poll of 3,619 randomly selected users of a social media site found that 2,463 users obtain most of their news about world events from this site. Research conducted in 2013 determined that 46% of all site users reported getting their news about world events from the site. 

##### Research Questions:
a. **Has the proportion of site users who get their world news from this site changed since 2013?**

   Instructions: Conduct a hypothesis test with a 0.05 significance level.

b. **What is the current proportion of site users getting most of their world news from the site in 2018?**

   Instructions: Construct a 95% confidence interval for the population proportion using the sample data. Reflect on how this confidence interval supports the hypothesis test conclusion.

##### Step-by-Step Analysis:

1. **State the Hypotheses**

   Let \( p \) represent the proportion of site users who get their world news from the site.

   - Null Hypothesis (\( H_0 \)): \( p = 0.46 \)
   - Alternative Hypothesis (\( H_a \)): \( p \neq 0.46 \)

   (Make sure to input the numbers accurately.)

2. **Compute the Test Statistic**

   Calculate the z-test statistic for the given data.

   - Formula: \( z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1-p_0)}{n}}}\)

   (Round to two decimal places as needed.)

3. **Compute the p-value**

   Determine the p-value based on the computed z-test statistic.

   (Round to three decimal places as needed.)

4. **Interpreting the Confidence Interval**

   - Construct a 95% confidence interval for the proportion of site users getting their news from the site in 2018.
   - Analyze how the confidence interval supports or contradicts your hypothesis test findings.

##### Conclusion:

Summarize the results of your hypothesis test and confidence interval analysis to address whether the proportion of site users obtaining their world news from this social media site has changed since 2013. Discuss any implications or trends indicated by the analysis.
Transcribed Image Text:### Educational Website Text #### Hypothesis Testing on Social Media News Consumption In 2018, a poll of 3,619 randomly selected users of a social media site found that 2,463 users obtain most of their news about world events from this site. Research conducted in 2013 determined that 46% of all site users reported getting their news about world events from the site. ##### Research Questions: a. **Has the proportion of site users who get their world news from this site changed since 2013?** Instructions: Conduct a hypothesis test with a 0.05 significance level. b. **What is the current proportion of site users getting most of their world news from the site in 2018?** Instructions: Construct a 95% confidence interval for the population proportion using the sample data. Reflect on how this confidence interval supports the hypothesis test conclusion. ##### Step-by-Step Analysis: 1. **State the Hypotheses** Let \( p \) represent the proportion of site users who get their world news from the site. - Null Hypothesis (\( H_0 \)): \( p = 0.46 \) - Alternative Hypothesis (\( H_a \)): \( p \neq 0.46 \) (Make sure to input the numbers accurately.) 2. **Compute the Test Statistic** Calculate the z-test statistic for the given data. - Formula: \( z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1-p_0)}{n}}}\) (Round to two decimal places as needed.) 3. **Compute the p-value** Determine the p-value based on the computed z-test statistic. (Round to three decimal places as needed.) 4. **Interpreting the Confidence Interval** - Construct a 95% confidence interval for the proportion of site users getting their news from the site in 2018. - Analyze how the confidence interval supports or contradicts your hypothesis test findings. ##### Conclusion: Summarize the results of your hypothesis test and confidence interval analysis to address whether the proportion of site users obtaining their world news from this social media site has changed since 2013. Discuss any implications or trends indicated by the analysis.
**Hypothesis Testing and Confidence Interval Interpretation**

**Reject \( H_0 \) or Do Not Reject \( H_0 \): Interpret the Conclusion**

Choose the correct answer below:

- **A.** Reject \( H_0 \). The percentage is not significantly different from 46%.
- **B.** Do not reject \( H_0 \). The percentage is significantly different from 46%.
- **C.** Do not reject \( H_0 \). The percentage is not significantly different from 46%.
- **D.** Reject \( H_0 \). The percentage is significantly different from 46%.

**Confidence Interval Calculation**

**b.** The 95% confidence interval for the population proportion is \( ( \, \_ \_ \_ \_ , \, \_ \_ \_ \_ \, ) \).

*(Round to four decimal places as needed.)*

The result of the 95% confidence interval \( \underline{\quad} \) with the result of the hypothesis test performed in part (a) because the value of \( p_0 \) is \( \underline{\quad} \) the 95% confidence interval.
Transcribed Image Text:**Hypothesis Testing and Confidence Interval Interpretation** **Reject \( H_0 \) or Do Not Reject \( H_0 \): Interpret the Conclusion** Choose the correct answer below: - **A.** Reject \( H_0 \). The percentage is not significantly different from 46%. - **B.** Do not reject \( H_0 \). The percentage is significantly different from 46%. - **C.** Do not reject \( H_0 \). The percentage is not significantly different from 46%. - **D.** Reject \( H_0 \). The percentage is significantly different from 46%. **Confidence Interval Calculation** **b.** The 95% confidence interval for the population proportion is \( ( \, \_ \_ \_ \_ , \, \_ \_ \_ \_ \, ) \). *(Round to four decimal places as needed.)* The result of the 95% confidence interval \( \underline{\quad} \) with the result of the hypothesis test performed in part (a) because the value of \( p_0 \) is \( \underline{\quad} \) the 95% confidence interval.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax