According to a Pew Research Center study, in May 2011, 33% of all American adults had 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 comm college students. She selects 352 community college students at random and finds that 12 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. 1. This is an example of a 2. Find the standard error. 3. Find the z value. V hypothesis test.

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**Understanding Hypothesis Testing in Statistics**

According to a Pew Research Center study conducted in May 2011, 33% of American adults possessed a smartphone capable of reading emails and surfing the Internet. A communications professor suspects that this percentage is lower among community college students. 

To test this hypothesis, she randomly selects a sample of 352 community college students and discovers that 122 of them own a smartphone. The hypotheses are set up as follows:

- **Null Hypothesis (H0):** p = 0.33 
- **Alternative Hypothesis (Ha):** p < 0.33

The hypothesis test is performed at a significance level of α = 0.05.

### Using Excel for Statistical Analysis

Follow these steps using Excel to determine the hypothesis test results for questions 3 and 4:

1. **Type of Hypothesis Test:**  
   Indicate if it’s a one-tailed or two-tailed test.
   
2. **Find the Standard Error:**  
   Calculate the standard error of the sample proportion.

3. **Find the Z Value:**  
   Determine the z value based on the sample data.

4. **Find the P-Value:**  
   Calculate the p-value to understand the statistical significance of the test.

These steps guide the process of assessing the professor’s belief statistically through hypothesis testing.
Transcribed Image Text:**Understanding Hypothesis Testing in Statistics** According to a Pew Research Center study conducted in May 2011, 33% of American adults possessed a smartphone capable of reading emails and surfing the Internet. A communications professor suspects that this percentage is lower among community college students. To test this hypothesis, she randomly selects a sample of 352 community college students and discovers that 122 of them own a smartphone. The hypotheses are set up as follows: - **Null Hypothesis (H0):** p = 0.33 - **Alternative Hypothesis (Ha):** p < 0.33 The hypothesis test is performed at a significance level of α = 0.05. ### Using Excel for Statistical Analysis Follow these steps using Excel to determine the hypothesis test results for questions 3 and 4: 1. **Type of Hypothesis Test:** Indicate if it’s a one-tailed or two-tailed test. 2. **Find the Standard Error:** Calculate the standard error of the sample proportion. 3. **Find the Z Value:** Determine the z value based on the sample data. 4. **Find the P-Value:** Calculate the p-value to understand the statistical significance of the test. These steps guide the process of assessing the professor’s belief statistically through hypothesis testing.
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