Question

Fifty athletes from all SPC athletic teams are randomly split into 2 teams. The first team is given a traditional training regimen. The second team is give an experimental training regimen. At the end of 6 weeks, the teams competed in 25 head-to-head 100m dash races pitting each person from the traditional regimen versus one person from the experimental regimen. At the end, the traditional regimen had won 9 of the races, the experimental regimen had won 14 of the races, and there were 2 ties. Is there sufficient evidence to support the claim that the Experimental regimen is more likely to result in faster athletes at the α=0.05 level of significance?

Question 11 options:

	Reject H1
	Fail to Reject H1
	Reject H0
	Fail to Reject H0

Answer 1

p1cap = X1/N1 = 9/50 = 0.18
p2cap = X2/N2 = 14/50 = 0.28
pcap = (X1 + X2)/(N1 + N2) = (9+14)/(50+50) = 0.23

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.18-0.28)/sqrt(0.23*(1-0.23)*(1/50 + 1/50))
z = -1.19

P-value Approach
P-value = 0.1170
As P-value >= 0.05, fail to reject null hypothesis.

Fail to Reject H0