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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_____________ .

Respuesta :

Solution:

Given;

[tex]\begin{gathered} n=400,x=136 \\ \\ x=number\text{ }of\text{ }successes,n=sample\text{ }size \end{gathered}[/tex]

Then, the true proportion, p, is;

[tex]\begin{gathered} p=\frac{x}{n} \\ \\ p=\frac{136}{400} \\ \\ p=0.34 \end{gathered}[/tex]

Now, we use the formula;

[tex]p\pm z_{\alpha}\sqrt{\frac{p(1-p)}{n}}[/tex]

Thus, we have;

[tex]0.34\pm1.96\sqrt{\frac{0.34(1-0.34)}{400}}[/tex]

Then;

[tex](0.294,0.386)[/tex]

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

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