Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 37 of the 42 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 98 of the 113 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections. Find the test statistic Z to two or more decimal places and the P-value to three or more places.

Answer 1

p1cap = X1/N1 = 37/42 = 0.881
p1cap = X2/N2 = 98/113 = 0.8673
pcap = (X1 + X2)/(N1 + N2) = (37+98)/(42+113) = 0.871

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 = (0.881-0.8673)/sqrt(0.871*(1-0.871)*(1/42 + 1/113))
z = 0.23

P-value Approach
P-value = 0.8181
As P-value >= 0.01, fail to reject null hypothesis.

There is no evidence to conclude that the echinacea has an effect on rhinovirus infections