a We have four surveys of randomly selected students who are taking the same class with us. According to the survey results, the students will decide the day of their tests (Monday or Friday). The survey question is whether they want to have the test on Friday. The results are given as follows.
Sample Size
Number of Yes Responses
Percent of Votes
10
8
80 %
20
12
60 %
30
16
53.3 %
40
18
45 %
We will consider whether the test will be on Friday by looking at the results of the first two surveys.
Sample Size
Number of Yes Responses
Percent of Votes
10
8
80 %
20
12
60 %
30
16
53.3 %
40
18
45 %
To have the test on Friday more than half of the students need to respond yes to the survey. In other words, to have the test on Friday the percent of yes votes should be more than 50 %.
Sample Size
Number of Yes Responses
Percent of Votes
10
8
80 %> 50 %
20
12
60 %> 50 %
30
16
53.3 %
40
18
45 %
Since the percent of the votes is more than 50 % based on the results of the first two survey, yes, the test will be on Friday.
b In this exercise, we will take account of the whole table, and we will think about whether the test will be on Friday. From the table we can see that when the sample size increases, the percent of votes to have the test on Friday decreases. Let's consider the survey with the larger sample space.
Sample Size
Number of Yes Responses
Percent of Votes
10
8
80
20
12
60
30
16
53.3 %
40
18
45 %
In the last survey, we can see that the percent of votes is 45 %, which is less than 50 %. Therefore, the percent is insufficient to have the test on Friday. The answer is no.
