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Practice A
Two-Way Tables

The table shows the results of a survey of 100 randomly-selected people entering an amusement park who were asked whether they were planning to ride the Monster Loop, a rollercoaster. Make a table of joint and marginal relative frequencies. The table has been started for you.

Ages 8-15
Ages 16-25
Ages 26-35
36 and Older

Yes
19
23
8
14

No
8
11
12
5

Ages 8-15
Ages 16-25
Ages 26-35
36 and Older
Total

Yes
0.19
0.27

204
0.64

No
O.Cll

theta
0.1

Total

1

Practice A $\newline$ Two-Way Tables $\newline$ $1$ . The table shows the results of a survey of $100$ randomly-selected people entering an amusement park who were asked whether they were planning to ride the Monster Loop, a rollercoaster. Make a table of joint and marginal relative frequencies. The table has been started for you. $\newline$ \begin{tabular}{|l|c|c|c|c|} $\newline$ \cline { $2$ - $5$ } \multicolumn{ $1$ }{c|}{} & Ages $8$ $-15$ & Ages $16$ $-25$ & Ages $26$ $-35$ & $36$ and Older \\ $\newline$ \hline Yes & $19$ & $23$ & $8$ & $14$ \\ $\newline$ \hline No & $8$ & $11$ & $12$ & $5$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ \begin{tabular}{|c|c|c|c|c|c|} $\newline$ \hline & Ages $8$ $-15$ & Ages $16$ $-25$ & Ages $26$ $-35$ & $36$ and Older & Total \\ $\newline$ \hline Yes & $0$ . $19$ & $0$ . $27$ & & $204$ & $0$ . $64$ \\ $\newline$ \hline No & O.Cll & $\theta$ & $0$ . $1$ & & \\ $\newline$ \hline Total & & & & & $1$ \\ $\newline$ \hline $\newline$ \end{tabular}

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Q. Practice A

\newline

Two-Way Tables

\newline

1

. The table shows the results of a survey of

100

randomly-selected people entering an amusement park who were asked whether they were planning to ride the Monster Loop, a rollercoaster. Make a table of joint and marginal relative frequencies. The table has been started for you.

\newline

\begin{tabular}{|l|c|c|c|c|}

\newline

\cline {

2

5

} \multicolumn{

1

}{c|}{} & Ages

8

-15

& Ages

16

-25

& Ages

26

-35

36

and Older \\

\newline

\hline Yes &

19

23

8

14

\newline

\hline No &

8

11

12

5

\newline

\hline

\newline

\end{tabular}

\newline

\begin{tabular}{|c|c|c|c|c|c|}

\newline

\hline & Ages

8

-15

& Ages

16

-25

& Ages

26

-35

36

and Older & Total \\

\newline

\hline Yes &

0

19

0

27

& &

204

0

64

\newline

\hline No & O.Cll &

\theta

0

1

& & \\

\newline

\hline Total & & & & &

1

\newline

\hline

\newline

\end{tabular}

Calculate Total Yes Responses: First, let's calculate the total number of people who said ＂Yes＂ to riding the Monster Loop. We add up the numbers across the ＂Yes＂ row: $19$ (Ages $8$ - $15$ ) + $23$ (Ages $16$ - $25$ ) + $8$ (Ages $26$ - $35$ ) + $14$ ( $8$ $0$ and Older) = $8$ $1$ .
Calculate Total No Responses: Next, calculate the total number of people who said ＂No＂ to riding the Monster Loop. We add up the numbers across the ＂No＂ row: $8$ (Ages $8$ - $15$ ) + $11$ (Ages $16$ - $25$ ) + $12$ (Ages $26$ - $35$ ) + $5$ ( $8$ $0$ and Older) = $8$ $0$ .
Calculate Marginal Relative Frequencies Ages $8$ $-15$ : Now, we calculate the marginal relative frequencies for each age group and response. We start with Ages $8$ $-15$ : Yes = $\frac{19}{100} = 0.19$ , No = $\frac{8}{100} = 0.08$ .
Calculate Marginal Relative Frequencies Ages $16$ $-25$ : For Ages $16$ $-25$ , calculate the relative frequencies: Yes = $\frac{23}{100} = 0.23$ , No = $\frac{11}{100} = 0.11$ .
Calculate Marginal Relative Frequencies Ages $26$ $-35$ : For Ages $26$ $-35$ , calculate the relative frequencies: Yes = $\frac{8}{100} = 0.08$ , No = $\frac{12}{100} = 0.12$ .
Calculate Marginal Relative Frequencies Ages $36$ and Older: For $36$ and Older, calculate the relative frequencies: Yes = $\frac{14}{100} = 0.14$ , No = $\frac{5}{100} = 0.05$ .
Calculate Total Relative Frequencies: Calculate the total relative frequencies for ＂Yes＂ and ＂No＂ responses: Yes = $\frac{64}{100} = 0.64$ , No = $\frac{36}{100} = 0.36$ .
Fill Completed Table: Fill in the completed table with the calculated values. However, there's a mistake in the provided values in the question prompt, where it says $204$ and $\theta$ which don't align with our calculations.