Question

I believe the proportion of summer competitors for a triathlon is greater in Connecticut compared to summer competitors for a triathlon in Florida.

Surveyed;

300 triathletes in CT, 180 participated in the summer event

264 triathletes in FL, 109 participated in the summer event

Answer 1

Let p1 be proportion of summer competitors for triathlon in Connecticut.

p2 be proportion of summer competitors for triathlon in Florida.

Let null hypothesis be

Ho: p1=p2

Against

Ha: p1>p2

Test statistics is

Z = (p1bar-p2bar) / sqrt((p1bar*(1-p1bar)/n1 +(p2bar*(1-p2bar)/n2)

Here p1 bar = 180/300 = 0.6

p2bar = 109/264 = 0.41

Z= (0.6-0.41) / sqrt( (0.6*0.4)/300 + (0.41*0.59)/264)

= 0.19 / 0.041

= 4.63

P value corresponding to one tailed z test is less than 0.00001. Since p value is less than 1% , we reject Ho at 1%. Hence we conclude that proportion of summer competitors for triathlon is greater in Connecticut compared to Florida.