1. Prompted by a curiosity over whether the current NFC South is the worst division in the history of the NFL, a sportswriter examines the distribution of Super Bowl wins by division. This is the number of Super Bowl wins by current NFL division: Division NFC East Super Bowl Wins 13 AFC East 9 AFC West 8 AFC North 8 NFC West 8 NFC North 5 NFC South 3 AFC South 2 Using this data ( = 0.05), determine if the distribution of Super Bowl wins across divisions is significantly different from uniform. In addition to your ultimate decision, include the chi-square statistic, degrees of freedom, and chi-square critical value. 2. Opticians are curious whether the type of vision correction that customers use is associated with how often they find themselves thinking about their vision. They ask four groups of vision correction consumers (eye glasses wearers, contact wearers, Lasik recipients, and people with no vision correction) about whether they think about their vision frequently, sometimes, or never. Using the data below, determine if there is a significant difference in vision consideration by type of vision correction ( = 0.05). In addition to your ultimate decision, include the chi-square statistic, degrees of freedom, and chi-square critical value. Vision Correction Glasses Contacts Lasik No Correction Total Frequently Sometimes Never Total 45 40 15 100 35 50 15 100 15 40 45 100 5 20 75 100 100 150 150 400 3. Consumer scientists are curious if there is a difference in level of complaints that employees receive by commercial sector. Observing 100 consumer-employee interactions, they document whether the consumer complained and the sector. Using the data below, determine if there is a significant difference in complaints by commercial sector ( = 0.05). In addition to your ultimate decision, include the chi-square statistic, degrees of freedom, and chi-square critical value. Sector Food Complained Did not Complain Total 15 10 25 Retail 10 10 20 Pharmacy 10 20 30 Tech Support 15 10 25 Total 50 50 100