Question

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 (pM − pE). Interpret the result.

Answer 1

Answer:  90% confidence interval would be $(-0.2483,-0.0717)$

Step-by-step explanation:

Since we have given that

n₁ = 50

Number of metal tagged penguins survived = 10

So, $p_m=\dfrac{10}{50}=0.2$

n₂ = 50

Number of electronic tagged penguins = 18

So, $p_e=\dfrac{18}{50}=0.36$

So, at 90% confidence interval, z = 1.28

So, interval would be

$(p_m-p_e)\pm z\sqrt{\dfrac{p_m(1-p_m)}{n}+\dfrac{p_e(1-p_e)}{n}}\\\\=(0.2-0.36)\pm 1.28\sqrt{\dfrac{0.2\times 0.8}{50}+\dfrac{0.36\times 0.64}{50}}\\\\=-0.16\pm 0.0883\\\\=(-0.16-0.0883,-0.16+0.0883)\\\\=(-0.2483,-0.0717)$

Hence, 90% confidence interval would be

$(-0.2483,-0.0717)$