Question 18
Competitive eating a very popular sport in Western Countries. Competitive eating, or speed eating, is a sport in which participants compete against each other to eat large quantities of food, usually in a short time period. There is a general myth that people who have larger waist sizes eat faster and hence have a better chance of winning such competitions. Hence, to check if this is a dependence between waist size and eating speed the data (as specified in Table-3) was collected from interested and willing participants. In this data, the time to complete a A2B Family Dosa (which is equivalent to ~4 Dosas) was considered. The time was grouped into three categories as (i) Fast (less than 2 mins), (ii) Medium (greater than 2 mins but less than 4 minutes) and (iii) Slow (a time greater than 4 minutes). The participants who took part in the study where categorised into five categories based on their waist size as (i) S, (ii) M, (iii) L, (iv) XL, (v) XXL. The entry in a cell indicates the number of participants who completed the dosa in the specified time bucket and have the indicated waist size. Given this information,answer the subquestions.
| Waist Size | Eating Speed | ||
|---|---|---|---|
| Fast | Medium | Slow | |
| S | 20 | 27 | 23 |
| M | 13 | 22 | 19 |
| L | 13 | 19 | 12 |
| XL | 20 | 27 | 22 |
| XXL | 18 | 24 | 21 |
Table-3
How many degrees of freedom is present for the test statistic, used to perform the desired hypothesis test