Question

You have asked a sample of men and women in your community whether or not they intend to vote for a gas tax to raise money for public transportation. Of the men, 15 said "yes" and 20 said "no"; of the women, 25 said "yes" and 10 said "no". Assuming that proper experimental procedures have been followed, what can you conclude?

(note: if you determine that the df = 1, or an expected frequency is less than 5, then you should use the Yates Correction in your calculation).

Choose the most correct answer.

Select one:

a. After performing a Yates Corrected 2 x 2 chi-square test, a statistically significant difference between men and women was found in terms of their opinions on a gas tax to fund public transportation (X² = 3.93, df = 1, p < 0.05).

b. After performing a Yates Corrected 2 x 2 chi-square test, a statistically significant difference between men and women was found in terms of their opinions on a gas tax to fund public transportation (X² = 5.83, df = 1, p < 0.05).

c. After performing a Yates Corrected 2 x 2 chi-square test, no statistically significant difference between men and women was found in terms of their opinions on a gas tax to fund public transportation (X² = 3.83, df = 1, p > 0.05).

d. After performing a Yates Corrected 2 x 2 chi-square test, a statistically significant difference between men and women was found in terms of their opinions on a gas tax to fund public transportation (X² = 4.73, df = 1, p < 0.05).

e. After performing a Yates Corrected 2 x 2 chi-square test, no statistically significant difference between men and women was found in terms of their opinions on a gas tax to fund public transportation (X² = 3.73, df = 1, p > 0.05).

Answer 1

observed values :

	yes	no
men	15	20
women	25	10

grand total = 15+20+25+10 = 70

expected values = sum of row * sum of column / grand total

expected values :

	yes	no
men	(15+20)*(15+25) / 70 = 20	(15+20)*(20+10) / 70 = 15
women	(25+10)*(15+25) / 70 = 20	(25+10)*(20+10) / 70 = 15

therefore,

chi-square test (corrected) using above formula

chi-square test (corrected) = 4.73

df = (rows - 1)*(columns - 1) = (2-1)*(2-1) = 1

p<0.05 (signifiacance level)

ANSWER : option d.

(please UPVOTE)