Question

Out of 400 animals sampled, 136 had a tail. Based on this, construct a 95% confidence interval for the true population proportion of animals with tails.Give your answers as decimals, to three placesI am 95% confident that the proportion of animals with tails is between _________ and_____________ .

Answer 1

Given;

`\begin{gathered} n=400,x=136 \\ \\ x=number\text{ }of\text{ }successes,n=sample\text{ }size \end{gathered}`

Then, the true proportion, p, is;

`\begin{gathered} p=(x)/(n) \\ \\ p=(136)/(400) \\ \\ p=0.34 \end{gathered}`

Now, we use the formula;

`p\pm z_(\alpha)\sqrt{(p(1-p))/(n)}`

Thus, we have;

`0.34\pm1.96\sqrt{(0.34(1-0.34))/(400)}`

Then;

`(0.294,0.386)`

ANSWER: I am 95% confident that the proportion of animals with tails is between 0.294 and 0.386