Question

a group of 125 students were asked whether they have a curfew and whether they have chores at home. their responses are summarized in the following table.

	have chores	dont have chores
dont have a curfew	39	21

(a) what percentage of the students have a curfew?
(b) what percentage of the students dont have chores?
(c) what percentage of the students who dont have chores have a curfew?
(d) is there evidence that students who dont have chores tend to have a curfew more often than average?
no, because the percentage found in part (c) is about the same as the percentage found in part (a).
no, because the percentage found in part (c) is about the same as the percentage found in part (b).
yes, because the percentage found in part (c) is much greater than the percentage found in part (a).
yes, because the percentage found in part (c) is much greater than the percentage found in part (b).

Explanation:

Step1: Calculate percentage of students with curfew

The total number of students is \(24 + 41+21 + 39=125\). The number of students with a curfew is \(24 + 41 = 65\). The percentage of students with a curfew is \(\frac{65}{125}\times100\%=52\%\).

Step2: Calculate percentage of students without curfew

The number of students without a curfew is \(21+39 = 60\). The percentage of students without a curfew is \(\frac{60}{125}\times100\% = 48\%\).

Step3: Calculate percentage of students with curfew and chores

The number of students with a curfew and chores is \(41\). The percentage is \(\frac{41}{125}\times100\%=32.8\%\).

Step4: Calculate percentage of students with curfew and no - chores

The number of students with a curfew and no - chores is \(24\). The percentage is \(\frac{24}{125}\times100\% = 19.2\%\).

Step5: Calculate percentage of students without curfew and with chores

The number of students without a curfew and with chores is \(39\). The percentage is \(\frac{39}{125}\times100\%=31.2\%\).

Step6: Calculate percentage of students without curfew and no - chores

The number of students without a curfew and no - chores is \(21\). The percentage is \(\frac{21}{125}\times100\%=16.8\%\).

Step7: Analyze if students without chores tend to have curfew more often

The percentage of students without chores who have a curfew is \(\frac{24}{24 + 21}\times100\%=\frac{24}{45}\times100\%\approx53.3\%\). The percentage of students with chores who have a curfew is \(\frac{41}{41+39}\times100\%=\frac{41}{80}\times100\% = 51.25\%\). Since \(53.3\%>51.25\%\), students who don't have chores tend to have a curfew more often.

Answer:

(a) \(52\%\)
(b) \(48\%\)
(c) \(31.2\%\)
(d) Yes, because the percentage of students who don't have chores and have a curfew (\(53.3\%\)) is greater than the percentage of students who have chores and have a curfew (\(51.25\%\))