According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is lower among communit college students. She selects 352 community college students at random and finds that 122 0 them have a smart phone. In testing the hypotheses: Ho: p= 0.33 versus Ha: p < 0.33 Do the hypothesis test. Use a level of significance of a = 0.05; Use the unrounded values in Excel to find the answers for #3 and # 4. 4. Find the p-value.-- 5. The communication professor should the null hypothesis.

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### Hypothesis Testing Example

According to a Pew Research Center study, in May 2011, 33% of all American adults had a smartphone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is lower among community college students. She selects 352 community college students at random and finds that 122 of them have a smartphone. In testing the hypotheses:

- **Null Hypothesis (Ho):** \( p = 0.33 \)
- **Alternative Hypothesis (Ha):** \( p < 0.33 \)

### Steps for Hypothesis Testing

1. **Significance Level:** Use a level of significance of \( \alpha = 0.05 \).

2. **Data Analysis:** Use the unrounded values in Excel to find the answers for the specific calculations needed in questions #3 and #4 (details not provided).

3. **Finding the p-value:** Perform the necessary calculations to determine the p-value.

4. **Conclusion:** Decide whether to reject or fail to reject the null hypothesis based on the p-value and the level of significance.

### Instructions for Excel

- Utilize Excel for precise calculations by entering the data about smartphone ownership among the selected students.
- Implement the formulas needed to find the p-value and determine the statistical significance of the results.

### Conclusion

The communication professor will use the results to conclude whether there is enough evidence to support her belief that the proportion of community college students with smartphones is less than the national average reported by the Pew Research Center in 2011. The action (reject or fail to reject) depends on the calculated p-value compared to the significance level.
Transcribed Image Text:### Hypothesis Testing Example According to a Pew Research Center study, in May 2011, 33% of all American adults had a smartphone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is lower among community college students. She selects 352 community college students at random and finds that 122 of them have a smartphone. In testing the hypotheses: - **Null Hypothesis (Ho):** \( p = 0.33 \) - **Alternative Hypothesis (Ha):** \( p < 0.33 \) ### Steps for Hypothesis Testing 1. **Significance Level:** Use a level of significance of \( \alpha = 0.05 \). 2. **Data Analysis:** Use the unrounded values in Excel to find the answers for the specific calculations needed in questions #3 and #4 (details not provided). 3. **Finding the p-value:** Perform the necessary calculations to determine the p-value. 4. **Conclusion:** Decide whether to reject or fail to reject the null hypothesis based on the p-value and the level of significance. ### Instructions for Excel - Utilize Excel for precise calculations by entering the data about smartphone ownership among the selected students. - Implement the formulas needed to find the p-value and determine the statistical significance of the results. ### Conclusion The communication professor will use the results to conclude whether there is enough evidence to support her belief that the proportion of community college students with smartphones is less than the national average reported by the Pew Research Center in 2011. The action (reject or fail to reject) depends on the calculated p-value compared to the significance level.
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