Question

6.148 A study tested whether applying metal tags is detrimental to penguins. One variable examined is the survival rate 10 years after tagging. The scientists observed that 10 of the 50 metal tagged penguins survived, compared to 18 of the 50 electronic tagged penguins. Construct a 90% confidence interval for the difference in proportion surviving between the metal and electronic tagged penguins (p_M – p_E). Interpret the result.

Answer 1

Here, , n1 = 50 , n2 = 50
p1cap = 0.2 , p2cap = 0.36

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.2 * (1-0.2)/50 + 0.36*(1-0.36)/50)
SE = 0.0884

For 0.9 CI, z-value = 1.64
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.2 - 0.36 - 1.64*0.0884, 0.2 - 0.36 + 1.64*0.0884)
CI = (-0.3050 , -0.0150)

As 0 is not included in the CI and CI is below 0. This indicates that there is significant difference in the two proportions.