Relative Frequency Table problem

Question

The following two-way table of row relative frequencies shows data on taking vitamin C supplements and contracting a cold for a group of 280  French skiers.

 

                      COLD          NO COLD          ROW TOTAL

No Vitamin C    0.22             0.78                 1.00

Vitamin C         0.15             0.85                 1.00

 

How many French skiers who were given vitamin C contracted colds? 

 

** I came up with 42 skiers (0.15)(280)=42 but the textbook answer says "not enough information." 

 

Not sure why...

 

 

Answer 1

Notice that there are Row Totals (1.00) but not Column Totals (??).  So, we do know that 0.15 of those who took Vitamin C got a cold (thus, your 0.15 is o.k.), but we don't know how many took Vitamin C (obviously, not all 280 took Vitamin C because there are numbers in the first row for those who did not take Vitamin C).

 

This is NOT what the problem says, but with proportions we can consider that there are 100 observations and the proportion represents them.  So, if the table had counts (not percentages) of people, the table would be:

 
                      COLD          NO COLD          ROW TOTAL
No Vitamin C     22                78                    100
Vitamin C          15                85                    100

 

With counts, not percentages, 100 people took Vitamin C and another 100 people did not.  And we know how many total got colds (37) and how many didn't (163).  However, when the two rows show percentages (as decimal fractions), we don't know the count of observations in each row.

 

Answer 2

The question really doesn't break down how many of the 280 were given C and how many were not.

 

The table only reflects the proportion of each of those groups getting sick.