Final answer:
To construct a two-way frequency table from the given survey data, we perform calculations to determine the number of people who went fishing and swimming, fishing but not swimming, not fishing but swimming, and neither fishing nor swimming. These figures are then organized into a table reflecting the two activities and their combinations among the survey respondents.
Step-by-step explanation:
The student is asking about how to construct a two-way frequency table based on the provided data about a group of people who visited a lake and their activities there. We can begin by calculating the number of people who went fishing and those who did not. Then we calculate the number of people who went swimming from each group.
Here are the calculations:
Total number of people surveyed: 120
Number of people who went fishing (20% of 120): 0.20 × 120 = 24
Number of people who went fishing and swimming (75% of 24): 0.75 × 24 = 18
Number of people who went fishing and did not go swimming (24 - 18): 6
Number of people who did not go fishing: 120 - 24 = 96
Number of people who did not go fishing and went swimming (50% of 96): 0.50 × 96 = 48
Number of people who did not go fishing and did not go swimming (96 - 48): 48
Based on these calculations, the two-way frequency table can be constructed as follows:
Swimming Not Swimming Total
Fishing18 6 24
Not Fishing 48 48 96
Total 66 54 120