Math  /  Data & Statistics

Question2. Of the 3,500 surveys sent out by the campaign team, 967 responses were recorded. The responses were compiled into a variety of two-way frequency tables for analysis by the campaign team, one of which is included below. The rows of the given table indicate age bands of the respondents, while the columns indicate whether or not the respondent intends to vote for the team's candidate. Each entry in the table gives the total number of respondents that fall into the overlap of that entry's row and column categories. \begin{tabular}{|c|c|c|c|c|} \hline & Yes & No & Undecided & Total \\ \hline 1824\mathbf{1 8 - 2 4} & 25 & 71 & 40 & 136 \\ \hline 2534\mathbf{2 5 - 3 4} & 88 & 80 & 32 & 200 \\ \hline 3544\mathbf{3 5 - 4 4} & 68 & 54 & 44 & 166 \\ \hline 4554\mathbf{4 5 - 5 4} & 79 & 64 & 30 & 173 \\ \hline 5564\mathbf{5 5 - 6 4} & 91 & 58 & 22 & 171 \\ \hline 65+\mathbf{6 5 +} & 66 & 44 & 21 & 121 \\ \hline Total & 407 & 371 & 189 & 967 \\ \hline \end{tabular} (a) [5 points] What is the relative frequency of respondents that are aged 35-44 and who plan to vote for the candidate? Round your answer to 4 decimal places. (b) [ 5 points] What is the relative frequency of respondents between the ages of 18-34 who are undecided on whether they plan to vote for the candidate? (c) [10 points] Should the candidate focus more of their campaign budget on advertisements to people in the 18-24 age bracket or the 65+65+ age bracket? Explain your answer using at least. two relative frequencies to justify your plan.

Studdy Solution

STEP 1

What is this asking? We're looking at survey results to figure out how many people in different age groups plan to vote for a candidate, and then using that info to decide which age group the candidate should focus on. Watch out! Don't mix up the numbers for "yes," "no," and "undecided" voters!
Also, remember that relative frequency is a proportion, not just the raw count.

STEP 2

1. Calculate the relative frequency of 35-44 year olds voting "yes".
2. Calculate the relative frequency of 18-34 year olds who are undecided.
3. Analyze which age group to target.

STEP 3

We're looking for the relative frequency, which means we want the proportion of people in the 35-44 age group who said "yes" compared to the total number of respondents.

STEP 4

The table shows that 68\textbf{68} people aged 35-44 plan to vote "yes." The total number of respondents is 967\textbf{967}.

STEP 5

To get the relative frequency, we divide the number of 35-44 year old "yes" voters by the total number of respondents: 689670.0704 \frac{\textbf{68}}{\textbf{967}} \approx \textbf{0.0704} Rounding to four decimal places, the relative frequency is 0.0704\textbf{0.0704}.

STEP 6

Now, we want to find the proportion of people aged 18-34 who are undecided.
First, we need to find the *total* number of people in the 18-24 and 25-34 age groups who are undecided.

STEP 7

From the table: * 40\textbf{40} people aged 18-24 are undecided. * 32\textbf{32} people aged 25-34 are undecided. * Adding these together, we get 40+32=72\textbf{40} + \textbf{32} = \textbf{72} undecided people in the 18-34 age range.

STEP 8

The total number of respondents is still 967\textbf{967}.
So, the relative frequency of undecided voters aged 18-34 is: 729670.0745 \frac{\textbf{72}}{\textbf{967}} \approx \textbf{0.0745}

STEP 9

Let's compare the "yes" voters in the 18-24 group and the 65+ group.
The 18-24 group had 25\textbf{25} "yes" votes out of 967\textbf{967} total respondents, giving a relative frequency of: 259670.0258 \frac{\textbf{25}}{\textbf{967}} \approx \textbf{0.0258}

STEP 10

The 65+ group had 66\textbf{66} "yes" votes, resulting in a relative frequency of: 669670.0683 \frac{\textbf{66}}{\textbf{967}} \approx \textbf{0.0683}

STEP 11

The 65+ group has a much higher relative frequency of "yes" voters (0.0683\textbf{0.0683}) than the 18-24 group (0.0258\textbf{0.0258}).

STEP 12

(a) The relative frequency of respondents aged 35-44 who plan to vote "yes" is 0.0704\textbf{0.0704}. (b) The relative frequency of respondents aged 18-34 who are undecided is 0.0745\textbf{0.0745}. (c) The candidate should focus on the 65+ age group.
They have a higher relative frequency of "yes" voters (0.0683\textbf{0.0683}) compared to the 18-24 age group (0.0258\textbf{0.0258}).

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