Question

An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?

Answer 1

Step 1

Given;

Step 2

When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).

`\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}`

Thus;

`\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}`

checking properly, the sample proportion =0.30, because

`\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}`

Answer; Option D

`0.30`