Question

In a recent poll, 360 people were asked if they liked dogs, and 38% said they did. Find the Margin of Error for this poll, at the 99% confidence level. Give your answer to four decimal places if possible.

Answer 1

Step-by-step explanation:

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The margin of error will be calculated using the formula below

`\begin{gathered} ME=z\sqrt{((1-p)p)/(n)} \\ where, \\ z(99\%)=2.576 \\ p=(38)/(100)=0.38 \\ n=360 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} ME=z\sqrt{p((1-p))/(n)} \\ ME=2.576(√((0.38(1-0.38)))/(360) \\ ME=0.06589 \\ ME\approx0.0659 \end{gathered}`

Hence,

The final answer is

`\begin{equation*} 0.0659 \end{equation*}`