Complete question :
A study was designed to test whether applying metal tags is detrimental to a penguin. 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 (). Let be the proportion of penguins with metal tags that survived and be the proportion of penguins with electronic tags that survived. Round your answers to three decimal places.
Answer:
(-0.305 ; - 0.015)
Step-by-step explanation:
Sample size, n1 = 50
x1 = 10
n2 = 50
x2 = 18
P1 = x1 / n1 = 10/50 = 0.2
P2 = x2 / n2 = 18 /50 = 0.36
1 - P1 = 0.8 ; 1 - P2 = 0.64
Zcritical at 90% = 1.645
Confidence interval :
(P1 - P2) ± Zcritical * standard error
Standard Error = sqrt[(p1(1-p1))/n1 + (p2(1-p2))/n2]
S.E = sqrt((0.2(0.8))/50 + 0.36(0.64))/50)
S.E = sqrt((0.0032 + 0.004608))
S. E = sqrt(0.007808)
S. E = 0.0883628
(0.2 - 0.36) ± (1.645 * 0.0883628)
-0.16 ± 0.145356806
Lower boundary = - 0.16 - 0.145356806 = −0.305356806
Upper boundary = - 0.16 + 0.145356806 = −0.014643194
(-0.305 ; - 0.015)
