We are asked to show the relative frequencies with respect to the shift, so we should make a row two-way relative frequency table. To do so, we should divide each frequency by the row total.
Response
Shift
Yes
No
Total
Day
68/100
32/100
100/100
Night
22/100
78/100
100/100
Total
90/200
110/200
200/200
Values in a two-way relative frequency table are usually written using percentages. Therefore, let's evaluate the quotients and multiply each value by 100 %.
Response
Shift
Yes
No
Total
Day
0.68* 100 %=68 %
0.32* 100 %=32 %
1* 100 %=100 %
Night
0.22* 100 %=22 %
0.78* 100 %=78 %
1* 100 %=100 %
Total
0.45* 100 %=45 %
0.55* 100 %=55 %
1* 100 %=100 %
Notice that the percents in each row add up to 100 % because we show the relative frequencies with respect to the shift.
Let's take a look at the two-way relative frequency table we made in Part A.
Response
Shift
Yes
No
Total
Day
68 %
32 %
100 %
Night
22 %
78 %
100 %
Total
45 %
55 %
100 %
We can see that among workers in the day shift, the percent of Yes responses is more than twice the percent of No responses.
Yes &> No
68 %&> 32 %
Next, among workers in the night shift, more than three quarters of them answered No.
Yes &< No
22 %& > 78 %
This suggests that there might be an association between the response and the shift. Workers in the day shift choose Yes more often and the majority of night shift workers choose No. This association is rather strong because the differences of the percentages are large.
