Question

Criminologists want to estimate the true percentage of first-degree murder trials in the Superior Courts of Massachusetts that result in conviction. A confidence interval for which of the following would be most appropriate for this estimate?

a. One proportion
b. The difference between two proportions
c. Linear Regression

Answer 1

Answer:

a. One proportion

Because we are interested in just one parameter: "true percentage of first-degree murder trials in the Superior Courts of Massachusetts that result in conviction"

Step-by-step explanation:

Previous concepts

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".  

For this case the best answer is

a. One proportion

Because we are interested in just one parameter: "true percentage of first-degree murder trials in the Superior Courts of Massachusetts that result in conviction"

$p$ represent the real population proportion of interest  

$\hat p$ represent the estimated proportion for the sample obtained

n is the sample size required

$z$ represent the critical value for the margin of error  

The population proportion have the following distribution  

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$  

The confidence interval would be given by this formula  

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$