Question

The National Football League (NFL) is conducting a survey of fan behavior by collecting a random sample of 240 NFL fans. One question asks fans if they have ever participated in a violent act in or around their favorite team's stadium. Nationally, 28% of NFL fans have participated in a violent act around their team’s stadium. The research finds that 14% of Green Bay Packers fans have committed a violent act on game day. Conduct a significance test to answer the research question: Is there a significant difference (a=.05) in the proportion of Green Bay Packers fans compared to the rest of the NFL fans that have participated in a violent act?

Answer 1

sample size = n = 240

Here hypothesis are

H₀ : p = 0.28

H_a : p 0.28

Here p is the proportion of Green Bay Packers fans that have participated in a violent act and p₀ = 0.28 is the proportion of NFL fans that have participated in a violent act

Standard error of proportion = sqrt [p₀* (1- p₀)/n] = sqrt [ 0.28 * (1-0.28)/240] = 0.0290

Test statistic

z = (0.14 - 0.28)/0.0290 = -4.83

p - value = 2 * P(Z < -4.83) = 0.000001

so here as p - value is very less than the alpha = 0.05 s o we conclude that there is a significant difference proportion of Green Bay Packers fans compared to the rest of the NFL fans that have participated in a violent act.