AP Stats 1 Question

Question

The way in which response options are presented in a question can affect a person's response. Two hundred randomly selected people were asked about their milk chocolate or dark chocolate preference. One hundred of the participants were randomly given the option of milk chocolate first and the remaining 100 participants were given the option of dark chocolate first. The results are given in the table.

Milk Chocolate Dark Chocolate

Milk chocolate option first	52	48
Dark chocolate option first	41	59

To conclude if the order in which options are presented in a question affects the answer, a two-proportion z-test was conducted. What is the correct p-value of the test?

Answer 1

Z = (p1-p2)-0 / sqrt( p(1-p)(1/n1+1/n2))

p1 = 52/(52+48) = 0.52

p2 = 41/(41+59) = 0.41

p = (52+48)/(200) = 0.5

1/n1 + 1/n2 = 1/100 + 1/100 = 1/50=0.02

p(1-p) = 0.25

sqrt( 0.25*0.02)=0.07071067811865475244008443621048

p1-p2 = 0.09

z=1.2727922061357855439215198517887

no difference between the proportions