Question

Instructors at a sports club were surveyed about whether they are certified in CPR. The survey results are shown in the two-way frequency table.

Does the data show an association between the type of instructor and a certification in CPR? PLEASE I NEED HELP

Answer 1

Answer: The data shows an association between the type of instructor and a certification in CPR. The association is that swimming instructors are less likely than tennis instructors to be certified in CPR. This can be seen from the frequency table, where all the swimming instructors are not certified in CPR, while only 4 out of 12 tennis instructors are not certified in CPR, so yes, the data does show an association between the type of instructor and a certification in CPR.

Explanation:

The two-way frequency table shows the number of instructors who are certified or not certified in CPR, broken down by type of instructor (swimming or tennis). The data in the table allows us to see the relationship between the two variables (type of instructor and certification in CPR) and whether there is an association between them.

An association means that the values of one variable are related to the values of another variable in some way. In this case, the type of instructor (swimming or tennis) is related to whether or not the instructor is certified in CPR. The data shows that the proportion of swimming instructors who are not certified in CPR (100%) is higher than the proportion of tennis instructors who are not certified in CPR (33%). This indicates that there is an association between type of instructor and certification in CPR, with swimming instructors being less likely to be certified in CPR than tennis instructors.

It is important to note that this association does not necessarily imply causation, meaning that being a swimming instructor does not cause one to not be certified in CPR, but it could be the other way around, or it could be due to some other factors that the data does not show.

Answer 2

The correct statement from the given options would be:

"There is an association. Swimming instructors are more likely than tennis instructors to be certified in CPR."

To determine if there is an association between the type of instructor and CPR certification from the data provided in the two-way frequency table, follow these steps:

1. Calculate the percentage of each type of instructor that is certified in CPR.

2. Compare these percentages to see if there is a significant difference.

The data given is:

- 14 out of 14 swimming instructors are certified in CPR.

- 4 out of 12 tennis instructors are certified in CPR.

Now calculate the percentages:

- For swimming instructors:
`\( (14)/(14) * 100\% = 100\% \)`of swimming instructors are certified in CPR.

- For tennis instructors:
`\( (4)/(12) * 100\% = 33.\overline{3}\% \)`of tennis instructors are certified in CPR.

Given these percentages, we can observe that a much higher percentage of swimming instructors are certified in CPR compared to tennis instructors. This suggests that there is an association between the type of instructor and CPR certification, specifically that swimming instructors are more likely to be certified in CPR than tennis instructors.