Chapter 10, Problem 13PT

a)

To determine

To create: a two-way frequency table

Answer to Problem 13PT

	District 1	District 2	Total
In favour	178	161	339
Against	47	145	192
Total	225	306	531

Explanation of Solution

Given: In district $1$ , $225$ residents responded to the survey

In favour of merger $=178$

In district $2$ , Total $=306$ , against the merger $=145$

Concept Used: A two-frequency table is used to show the frequencies of data from survey.

Calculation: Total In district $1$ , $225$ residents and in district $2$ , Total $=306$

Total= $225+306=531$

In district $2$ , Total $=306$ and against the merger $=145$

In favour $306-145=161$

In district $1$ , In favour of merger $=178$ , total $=225$ residents

In against $225-178=47$

In favour subtotal $=178+161=339$

In Against subtotal $=47+145=192$

Conclusion:

	District 1	District 2	Total
In favour	178	161	339
Against	47	145	192
Total	225	306	531

b)

To determine

To create: a relative frequency table

Answer to Problem 13PT

	District 1	District 2	Total
In favour	$\frac{178}{531}.100\%\approx 34\%$	$\frac{161}{531}.100\%\approx 30\%$	$\frac{339}{531}.100\%\approx 64\%$
Against	$\frac{47}{531}.100\%\approx 9\%$	$\frac{145}{531}.100\%\approx 27\%$	$\frac{192}{531}.100\%\approx 36\%$
Total	$\frac{225}{531}.100\%\approx 42\%$	$\frac{306}{531}.100\%\approx 58\%$	$\frac{531}{531}.100\%\approx 100\%$

Explanation of Solution

Given: In district $1$ , $225$ residents responded to the survey

In favour of merger $=178$

In district $2$ , Total $=306$ , against the merger $=145$

Concept Used: A two way relative frequency table is the table in which each cell is divided by total and multiplies by 100%.

Calculation: For relative frequency table divide each cell by total $531$ and divide by $100\%$

Conclusion:

	District 1	District 2	Total
In favour	$\frac{178}{531}.100\%\approx 34\%$	$\frac{161}{531}.100\%\approx 30\%$	$\frac{339}{531}.100\%\approx 64\%$
Against	$\frac{47}{531}.100\%\approx 9\%$	$\frac{145}{531}.100\%\approx 27\%$	$\frac{192}{531}.100\%\approx 36\%$
Total	$\frac{225}{531}.100\%\approx 42\%$	$\frac{306}{531}.100\%\approx 58\%$	$\frac{531}{531}.100\%\approx 100\%$

c)

To determine

To create: a conditional frequency table for districts and responses

Answer to Problem 13PT

	District 1	District 2
In favour	$\frac{178}{225}.100\%\approx 79.1\%$	$\frac{161}{306}.100\%\approx 52.6\%$
Against	$\frac{47}{225}.100\%\approx 20.9\%$	$\frac{145}{306}.100\%\approx 47.4\%$
Total	$\frac{225}{225}.100\%\approx 100\%$	$\frac{306}{306}.100\%\approx 100\%$

	District 1	District 2	Total
In favour	$\frac{178}{339}.100\%\approx 52.5\%$	$\frac{161}{339}.100\%\approx 47.5\%$	$\frac{339}{339}.100\%\approx 100\%$
Against	$\frac{47}{192}.100\%\approx 24.5\%$	$\frac{145}{192}.100\%\approx 75.5\%$	$\frac{192}{192}.100\%\approx 100\%$

Explanation of Solution

Given: In district $1$ , $225$ residents responded to the survey

In favour of merger $=178$

In district $2$ , Total $=306$ , against the merger $=145$

Concept Used: For conditional relative frequency table divide each column and row by their total and divide by $100\%$

Calculation: For conditional frequency table for districts divide each column by their total and multiply by $100\%$

For conditional frequency table for responses divide each row by their total and multiply by $100\%$ .

Conclusion:

	District 1	District 2
In favour	$\frac{178}{225}.100\%\approx 79.1\%$	$\frac{161}{306}.100\%\approx 52.6\%$
Against	$\frac{47}{225}.100\%\approx 20.9\%$	$\frac{145}{306}.100\%\approx 47.4\%$
Total	$\frac{225}{225}.100\%\approx 100\%$	$\frac{306}{306}.100\%\approx 100\%$

	District 1	District 2	Total
In favour	$\frac{178}{339}.100\%\approx 52.5\%$	$\frac{161}{339}.100\%\approx 47.5\%$	$\frac{339}{339}.100\%\approx 100\%$
Against	$\frac{47}{192}.100\%\approx 24.5\%$	$\frac{145}{192}.100\%\approx 75.5\%$	$\frac{192}{192}.100\%\approx 100\%$