(a) Suppose we can consider this an SRS of all U.S. col- lege students. Make a stemplot. Is there any sign of major deviation from Normality? (b) Give a 95% confidence interval for the mean rating. (c) Is there significant evidence at the 5% level that the mean rating is greater than 3.5 (a neutral rating)?

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**Title: Trustworthiness Ratings of Mitt Romney by College Students**

**Introduction:**
Twenty-nine college students, identified as having a positive attitude towards Mitt Romney as compared to Barack Obama during the 2012 presidential election, were asked to rate the trustworthiness of Mitt Romney's face. Ratings were on a scale from 0 to 7, with 0 indicating "not at all trustworthy" and 7 indicating "extremely trustworthy." Below are the 29 ratings:

**Ratings Data:**
- 2.6, 3.2, 3.7, 3.3, 3.4, 3.6, 3.7, 3.8, 3.9, 4.1
- 4.2, 4.9, 5.7, 4.2, 3.9, 3.2, 4.5, 5.0, 5.0, 4.6
- 4.6, 3.9, 3.9, 5.3, 2.8, 2.6, 3.0, 3.3, 3.7

**Exercises:**

(a) **Statistical Representation:**
Assume that these ratings represent a Simple Random Sample (SRS) of all U.S. college students. Create a stem plot of the data. Analyze whether there are any significant deviations from a normal distribution.

(b) **Confidence Interval:**
Calculate a 95% confidence interval for the mean trustworthiness rating.

(c) **Hypothesis Testing:**
Assess whether there is significant evidence at the 5% significance level to conclude that the mean rating is greater than 3.5 (considered a neutral rating).

**Explanation of Techniques:**

- **Stem Plot:** A tool for visualizing data distribution and identifying outliers or skewness in the dataset.
  
- **Confidence Interval:** Provides a range within which the true mean rating likely falls, offering insight into the precision of the sampled data.
  
- **Hypothesis Testing:** A method to statistically determine whether the mean rating significantly exceeds a specified value, in this instance, 3.5.

--- 

This explanation provides an overview of the study conducted and guides students through data analysis exercises related to the perceptions of Mitt Romney's trustworthiness.
Transcribed Image Text:--- **Title: Trustworthiness Ratings of Mitt Romney by College Students** **Introduction:** Twenty-nine college students, identified as having a positive attitude towards Mitt Romney as compared to Barack Obama during the 2012 presidential election, were asked to rate the trustworthiness of Mitt Romney's face. Ratings were on a scale from 0 to 7, with 0 indicating "not at all trustworthy" and 7 indicating "extremely trustworthy." Below are the 29 ratings: **Ratings Data:** - 2.6, 3.2, 3.7, 3.3, 3.4, 3.6, 3.7, 3.8, 3.9, 4.1 - 4.2, 4.9, 5.7, 4.2, 3.9, 3.2, 4.5, 5.0, 5.0, 4.6 - 4.6, 3.9, 3.9, 5.3, 2.8, 2.6, 3.0, 3.3, 3.7 **Exercises:** (a) **Statistical Representation:** Assume that these ratings represent a Simple Random Sample (SRS) of all U.S. college students. Create a stem plot of the data. Analyze whether there are any significant deviations from a normal distribution. (b) **Confidence Interval:** Calculate a 95% confidence interval for the mean trustworthiness rating. (c) **Hypothesis Testing:** Assess whether there is significant evidence at the 5% significance level to conclude that the mean rating is greater than 3.5 (considered a neutral rating). **Explanation of Techniques:** - **Stem Plot:** A tool for visualizing data distribution and identifying outliers or skewness in the dataset. - **Confidence Interval:** Provides a range within which the true mean rating likely falls, offering insight into the precision of the sampled data. - **Hypothesis Testing:** A method to statistically determine whether the mean rating significantly exceeds a specified value, in this instance, 3.5. --- This explanation provides an overview of the study conducted and guides students through data analysis exercises related to the perceptions of Mitt Romney's trustworthiness.
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