Question

Rhino viruses typically cause common colds. In a test of the effectiveness of​ echinacea, 38 of the 43 subjects treated with echinacea developed rhinovirus infections. In a placebo​ group, 81 of the 96 subjects developed rhinovirus infections. Use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Identify the test statistic.

Answer 1

H0: p1 = p2
Ha: p1 not = p2

Here, x1 = 38 , x2 = 81 , n1 = 43 , n2 = 96
p1cap = 0.8837 , p2cap = 0.8438

pcap = (x1 + x2)/(n1 + n2)
pcap = (38 + 81)/(43 + 96)
pcap = 0.8561

Standard Error,
SE = sqrt(pcap * (1-pcap) * (1/n1 + 1/n2))
SE = sqrt(0.8561 * (1-0.8561) * (1/43 + 1/96))
SE = 0.0644

Test statistic,
z = (p1cap - p2cap)/SE
z = (0.8837 - 0.8438)/0.0644
z = 0.62

p-value = 2*P(z > 0.62) = 0.5353

Fail to reject H0
There is not sufficient eviedence to conclude that there is difference in the proportion