Researchers observed 15,824 individuals in malls, schools, stadiums, and other public places, recording whether each person smiled within 10 seconds. Table 22 compares their observations and the researchers€™ estimates of the individuals€™ ages.

Suppose one participant from the study is randomly selected.
a. Find P (smile | ages 0-10 years).
b. Find P (smile | ages 11-20 years).
c. Find P (smile | ages 21-40 years).
d. Find P (smile | ages 41-60 years).
e. Find P (smile | over age 60 years).
f. Describe a key pattern in the results you found in parts (a) through (e). What does the pattern mean in this situation? Can causation be assumed? Explain.
g. If the population is all Americans, what type(s) of bias likely occurred? Explain.

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Table 22 Smiling versus Age Group Age Group lyears) 0-10 11-20 21-40 41-60 over 60 Total 131 1748 1691 937 5226029 Smiling Not smiling 1187 2020 2955 2124 1509 Total2 2318 3768 4646 3061 2031 15,824