Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

The 9th-grade class was surveyed about their plans after high school graduation. The table describes the results.

\begin{tabular}{|c|l|l|l|}
\hline
& Plans to live at home & Plans to live on their own & Row Totals \\
\hline
Plans to attend college & [tex]$35\%$[/tex] & [tex]$30\%$[/tex] & [tex]$65\%$[/tex] \\
\hline
Plans not to attend college & [tex]$25\%$[/tex] & [tex]$10\%$[/tex] & [tex]$35\%$[/tex] \\
\hline
Column Totals & [tex]$50\%$[/tex] & [tex]$40\%$[/tex] & [tex]$100\%$[/tex] \\
\hline
\end{tabular}

Part A: Find the conditional relative frequency of a student who plans to live at home, given that they plan to attend college. (3 points)

Part B: Is there an association between attending college and living at home? (3 points)

Sagot :

GinnyAnswer
Sure, let's go through the solution step-by-step:

Part A: Find the conditional relative frequency of a student who plans to live at home, given that they plan to attend college.

To find the conditional relative frequency, we need to determine the probability of a student living at home given that they plan to attend college. This is found using the formula:

[tex]\[ P(\text{Live at Home} | \text{Attend College}) = \frac{P(\text{Live at Home and Attend College})}{P(\text{Attend College})} \][/tex]

From the table, we have the following data:
- \( P(\text{Attend College}) = 65\% = 0.65 \)
- \( P(\text{Live at Home and Attend College}) = 35\% = 0.35 \)

Using the formula:

[tex]\[ P(\text{Live at Home} | \text{Attend College}) = \frac{0.35}{0.65} \][/tex]

Performing the division:

[tex]\[ P(\text{Live at Home} | \text{Attend College}) = 0.538 \][/tex]

Thus, the conditional relative frequency is approximately \( 0.538 \) or \( 53.8\% \).

Part B: Is there an association between attending college and living at home?

To determine if there is an association between attending college and living at home, we can compare the conditional probability found in Part A with the overall probability of living at home.

From the table, we have:
- \( P(\text{Live at Home}) = 50\% = 0.50 \)

We know:
- \( P(\text{Live at Home} | \text{Attend College}) = 0.538 \)

There is an association if the probability of living at home given that a student attends college is different from the overall probability of living at home.

Since \( P(\text{Live at Home} | \text{Attend College}) \approx 0.538 \) is not equal to \( P(\text{Live at Home}) = 0.50 \), this indicates that the probability is indeed different, confirming an association.

Conclusion:

1. The conditional relative frequency of a student who plans to live at home, given that they plan to attend college, is approximately \( 0.538 \) or \( 53.8\% \) (Part A).
2. There is an association between attending college and living at home since [tex]\( 0.538 \)[/tex] is different from [tex]\( 0.50 \)[/tex] (Part B).
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.