Question

2 jada surveyed 300 people from various age groups about their shoe preferences. the two - way table summarizes the results of the survey.
jada concludes that there is a possible association between age and shoe preference. is jadas conclusion reasonable? explain your reasoning.
3 the two - way table summarizes data on writing utensil preference and the dominant hand for a sample of 100 people.
is there a possible association between the dominant hand and writing utensil preference? explain your reasoning.

Explanation:

Step1: Analyze the proportion of shoe preference by age group

For 4 - 10 years old:
The proportion of preferring sneakers (with or without laces) is \(\frac{21 + 12}{36}=\frac{33}{36}=\frac{11}{12}\approx0.92\).
For 11 - 17 years old:
The proportion of preferring sneakers (with or without laces) is \(\frac{21+48}{108}=\frac{69}{108}=\frac{23}{36}\approx0.64\).
For 18 - 24 years old:
The proportion of preferring sneakers (with or without laces) is \(\frac{15 + 54}{156}=\frac{69}{156}=\frac{23}{52}\approx0.44\).

Step2: Analyze the proportion of writing utensil preference by dominant hand

For left - handed:
The proportion of preferring pen is \(\frac{7}{13}\approx0.54\).
For right - handed:
The proportion of preferring pen is \(\frac{82}{87}\approx0.94\).

Answer:

Jada's conclusion is reasonable. The proportion of people preferring sneakers (with or without laces) changes with different age groups. For the writing utensil preference and dominant hand, there is a possible association. The proportion of right - handed people preferring pen (\(\frac{82}{87}\approx0.94\)) is much higher than that of left - handed people preferring pen (\(\frac{7}{13}\approx0.54\)).