(Solved): The general formula for a confidence interval is: Sample Statistic \( \pm z^{*} \). SE Where \( z^{ ...

The general formula for a confidence interval is: Sample Statistic \( \pm z^{*} \). SE Where \( z^{*} \) is sometimes referred to as the critical value and is chosen so that the proportion between \( -z^{*} \) and \( +z^{*} \) in the standard normal distribution is the confidence level. This is more accurate than using \( 2 \times \) SE for the margin of error from earlier in the course. Calculate the lower and upper limits of a \( 90 \% \) confidence interval for a population proportion given: \[ \hat{p}=0.46, S E=0.12 \] \( 90 \% \) Confidence interval \( =1 \) Round your answer to 3 decimal place. For an example of how to do a calculation like this see What inference can we make about a \( 90 \% \) confidence interval in general? (No answer given) The general form for a confidence interval is: Sample Statistic \( \pm z^{*} \). SE where \( -z^{*} \& z^{*} \) are the values on a Standard Normal Distribution, \( \mathcal{N}(0,1) \) that the Confidence Level \% lies between. An example for a \( 95 \% \) confidence interval can be seen in the picture below. Here we can see the \( -z^{*} \& z^{*} \) on the horizontal axis, \( -1.960 \) and \( 1.960 \). Consider how this relates back to our \( 95 \% \) rule that says approximately \( 95 \% \) of the normal distribution is between 2 standard deviations either side of the mean. What are the \( -z^{*} \) and \( z^{*} \) values for an \( 85 \% \) confidence interval \( \pm 2.054 \) \( \pm 1.44 \) What are the \( -z^{*} \) and \( z^{*} \) values for an \( 85 \% \) confidence interval \( \pm 2.054 \) \( \pm 1.44 \) \( \pm 1.645 \) \( \pm 1.881 \) \( \pm 1.555 \)