**Educational Website Transcript****Title: Understanding Hypothesis Testing and Confidence Intervals****Introduction:**A popular theory suggests that presidential candidates have an advantage if they are taller than their main opponents. Below is a dataset of heights (in centimeters) of randomly selected presidents along with the heights of their main opponents. Consider the following analysis:**Dataset:**- **Height (cm) of President:** 191, 175, 173, 191, 190, 175- **Height (cm) of Main Opponent:** 178, 181, 165, 184, 193, 185**Analysis:****(a) Hypothesis Testing:**1. **P-Value Analysis:** - Since the P-value is **greater than** the significance level, we **fail to reject** the null hypothesis. - Conclusion: There **is not** sufficient evidence to support the claim that presidents tend to be taller than their opponents.**(b) Confidence Interval Construction:**1. **Confidence Interval:** - The confidence interval is [___] cm < μd < [___] cm. - (Round to one decimal place as needed.)2. **Feature Leading to Conclusion:** - The confidence interval contains **zero**. - This leads us to **fail to reject** the null hypothesis.**Conclusion:**This analysis demonstrates the application of hypothesis testing and confidence intervals in evaluating claims based on statistical data. In this case, there is no significant evidence to support the theory that presidential candidates are generally taller than their main opponents. **Educational Website Content: Analyzing Presidential Height Advantage**A popular theory suggests that presidential candidates may have an advantage if they are taller than their main opponents. Below, we examine data on the heights (in centimeters) of randomly selected presidents and their primary opponents. This analysis will help us understand if there is statistical significance to the theory.**Height Data:**| President (cm) | Main Opponent (cm) ||----------------|---------------------|| 191 | 178 || 175 | 181 || 173 | 165 || 191 | 184 || 190 | 193 || 175 | 185 |**Statistical Analysis Tasks:**- **Identify the test statistic:** - Calculate \( t \) to two decimal places as needed.- **Identify the P-value:** - Calculate the P-value to three decimal places as required.**Hypothesis Test Conclusion:**- Since the P-value is [greater than/less than] the significance level, we [fail to reject/reject] the null hypothesis. There [is/is not] sufficient evidence to support the claim that taller presidential candidates have an advantage. Complete the analysis by filling in the blanks using statistical methods to determine the test statistic and P-value, thereby leading to a conclusion regarding the hypothesis.

For President:For Main opponent:Test statistic, t= 0.28 p-value at t= 0.28 and n1+n2-2= 6+6-2= 10 df is 0.782 95% confidence interval for mean: ((x̄1-x̄2)+-t*√s12/n1 +s22/n2 ) t at 0.05 and 10 df is 2.228 =>(1.5-2.228*5.2836 , 1.5+2.228*5.2836) (-10.2718, 13.2718) =>(-10.3, 13.3)