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A group of 250 students were asked whether they have a curfew and whether they have chores at home. Their responses are summarized in the following table.

\begin{tabular}{|c|c|c|}
\cline { 2 - 3 } \multicolumn{1}{c|}{} & Have chores & Don't have chores \\
\hline Have a curfew & 52 & 63 \\
\hline Don't have a curfew & 58 & 77 \\
\hline
\end{tabular}

(a) What percentage of the students have a curfew? [tex]$\square$[/tex] \%

(b) What percentage of the students don't have chores? [tex]$\square$[/tex] \%

(c) What percentage of the students who don't have chores have a curfew? [tex]$\square$[/tex] \%

(d) Is there evidence that students who don't 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).



Answer :

GinnyAnswer
Let's break down the question into parts and solve it step-by-step.

(a) What percentage of the students have a curfew?

To find this percentage, we need to add up all the students who have a curfew and then divide by the total number of students. From the table:
- Students who have a curfew and have chores: 52
- Students who have a curfew and don't have chores: 63

Total number of students who have a curfew:
[tex]\[ 52 + 63 = 115 \][/tex]

Now, divide by the total number of students (250) and then multiply by 100 to get the percentage:
[tex]\[ \frac{115}{250} \times 100 = 46\% \][/tex]

So, the percentage of students who have a curfew is:
[tex]\[ \boxed{46\%} \][/tex]

(b) What percentage of the students don't have chores?

To find this percentage, we need to add up all the students who don't have chores and then divide by the total number of students. From the table:
- Students who don't have a curfew and don't have chores: 77
- Students who have a curfew and don't have chores: 63

Total number of students who don't have chores:
[tex]\[ 63 + 77 = 140 \][/tex]

Now, divide by the total number of students (250) and then multiply by 100 to get the percentage:
[tex]\[ \frac{140}{250} \times 100 = 56\% \][/tex]

So, the percentage of students who don't have chores is:
[tex]\[ \boxed{56\%} \][/tex]

(c) What percentage of the students who don't have chores have a curfew?

To find this percentage, we consider only the students who don't have chores, and then find out what proportion of them have a curfew. From part (b), we know there are 140 students who don't have chores. From the table, 63 of these 140 students have a curfew.

So, we calculate:
[tex]\[ \frac{63}{140} \times 100 = 45\% \][/tex]

Thus, the percentage of students who don't have chores and have a curfew is:
[tex]\[ \boxed{45\%} \][/tex]

(d) Is there evidence that students who don't have chores tend to have a curfew more often than average?

For this, we compare the percentage of students who don't have chores and have a curfew (from part (c)) with the overall percentage of students who have a curfew (from part (a)).

- Percentage found in part (c): 45%
- Percentage found in part (a): 46%

Since the percentages are very close to each other, there doesn't seem to be a significant difference.

There is evidence that students who don't have chores do not tend to have a curfew more often than average. Therefore, the correct conclusion is:
[tex]\[ \boxed{\text{No, because the percentage found in part (c) is about the same as the percentage found in part (a).}} \][/tex]

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