Question

a random sample of 180 adults and children was surveyed about their preferred method of communication. the data are summarized in the row conditional relative frequency table for preferred communication method by age group.

	text messages	video chats	phone calls	emails	social media	total
children	0.4300	0.1900	0.1100	0.0500	0.2200	1.0000
total	0.3333	0.1389	0.2278	0.1389	0.1611	1.0000

indicate whether each statement is true or false

statement	true	false
the table proves that being a child causes texting to be the preferred method of communication
the table shows that more children than adults chose video chats as their preferred method of communication.

Explanation:

Step1: Analyze the first statement

To check for an association between age and preferred communication method, we compare the row conditional relative frequencies. For example, the proportion of adults preferring text messages (0.2125) is different from children (0.4300), and similar differences exist for other methods. So, there is evidence of an association. Thus, the first statement is True.

Step2: Analyze the second statement

A survey (observational data) can show an association but not prove causation. Just because children have a higher preference for texting doesn't mean being a child causes that preference (other factors could be involved). So, the second statement is False.

Step3: Analyze the third statement

The table has row conditional relative frequencies (proportions within each age group), not the actual number of children and adults. We don't know the number of children and adults (only the total sample size of 180, but not the split). For example, if there are far more adults than children, even with a lower proportion, adults could have more people preferring video chats. So, we can't conclude more children than adults chose video chats. Thus, the third statement is False.

Answer:

1. The table provides evidence of an association between age and the preferred method of communication: True
2. The table proves that being a child causes texting to be the preferred method of communication: False
3. The table shows that more children than adults chose video chats as their preferred method of communication: False