Question

residents of four cities are able to vote in an upcoming regional election. a newspaper recently conducted a survey to gauge support for each of the two candidates. the results of the poll are shown in the two - way frequency table below.

	candidate a	candidate b	total
carsonville	205	266	471
appleton	260	203	463
new thomas	180	138	318
total	797	805	1602

based on the data shown, which of the following statements are true?
i. the two cities with the highest number of respondents both show more support for candidate a.
ii. the number of people who support candidate b in carsonville is twice the number of people who support candidate b in new thomas.
iii. more residents of center city responded to the poll than the number who responded from new thomas.
iv. overall, more residents support candidate a than candidate b.
a. ii and iii
b. iii only
c. ii and iv
d. i and iv

Explanation:

Step1: Analyze statement I

The two cities with the highest number of respondents are Carsonville (471) and Appleton (463). In Carsonville, 266 support candidate B and 205 support candidate A. In Appleton, 260 support candidate A and 203 support candidate B. So, not both cities show more support for candidate A. Statement I is false.

Step2: Analyze statement II

The number of people who support candidate B in Carsonville is 266, and in New Thomas is 138. $266
eq2\times138$. Statement II is false.

Step3: Analyze statement III

The number of residents of Center - City who responded is 350, and from New Thomas is 318. Since $350>318$, more residents of Center City responded to the poll than the number who responded from New Thomas. Statement III is true.

Step4: Analyze statement IV

The total number of people who support candidate A is 797, and for candidate B is 805. So, more residents support candidate B than candidate A. Statement IV is false.

Answer:

B. III only