Chapter 11.5, Problem 7E

To determine

To predict the winner or tell whether the election is too close

Answer to Problem 7E

The treasurer and controller are too close

Explanation of Solution

Given information : The question is

The results are shown in table

Position	Leading candidate	Trailing candidate	Margin of error
Mayor	$56\%$	$44\%$	$\pm 3.5\%$
Treasurer	$53\%$	$47\%$	$\pm 4\%$
Sheriff	$55\%$	$45\%$	$\pm 4\%$
Controller	$54\%$	$46\%$	$\pm 6\%$

Calculation :

Position	Leading candidate	Margin of error	Interval
Mayor	$56\%$	$\pm 3.5\%$	$52.5\%-59.5\%$
Treasurer	$53\%$	$\pm 4\%$	$49\%-57\%$
Sheriff	$55\%$	$\pm 4\%$	$51\%-59\%$
Controller	$54\%$	$\pm 6\%$	$48\%-60\%$

Position	Trailing candidate	Margin of error	Interval
Mayor	$44\%$	$\pm 3.5\%$	$40.5\%-47.5\%$
Treasurer	$47\%$	$\pm 4\%$	$43\%-51\%$
Sheriff	$45\%$	$\pm 4\%$	$41\%-49\%$
Controller	$46\%$	$\pm 6\%$	$40\%-52\%$

Position	Winner prediction
Mayor	Leading candidate
Treasurer	Too close
Sheriff	Leading candidate
Controller	Too close