Final answer:
A two-way table is constructed with rows for male and female students, columns for whether they play an instrument, and the marginal frequencies at the end of rows and columns based on the survey of 40 students.
Step-by-step explanation:
To create a two-way table that includes the marginal frequencies based on the information given, we need to categorize the data into rows for gender (male, female) and columns for whether the students play an instrument (Yes, No). Given that 17 students in the survey play an instrument and 8 of them are male, we can infer that 17 - 8 = 9 female students play an instrument. Similarly, if 13 females do not play an instrument and there are a total of 40 students, then the number of males who do not play an instrument is 40 - 13 - 8 - 9 = 10. Lastly, for marginal frequencies, we add together the totals for each row and column.
The Two-Way Table
GenderPlays an Instrument (Yes)Does Not Play an Instrument (No)Total (Marginal Frequency)Male81018Female91322Total (Marginal Frequency)172340
In the table above, the bottom row and the rightmost column show the marginal frequencies, representing totals for each gender and choice of playing an instrument, respectively.