# Point Estimate & Confidence Interval

Assignment 3 Point Estimate and Confidence Interval

Consider the following two scenarios and respond to the questions that follow using the standard normal curve and formula for calculating confidence intervals.
1. Researchers from the Legal Studies department conducted a study to examine factors that predict prosecutorial decision making among prosecutors in Mississippis lower courts. The aim of the study was to examine whether prosecutorial decision is influenced by extra-legal factors such race, gender, age, and ethnicity. The sample size was 250 selected randomly from the population of prosecutors in the lower courts. The main instrument for data collection was questionnaire. One question on the questionnaire asked how much are you paid each year? This question was used to measure the annual income of the prosecutors in the sample. Using a simple analysis, the following summary statistics were produced for this item (annual income): Mean annual income was \$55,000.00 and a standard deviation of \$5,000.00. Respond to the following:

a. Using 95% confidence level, determine the confidence interval within which the true population mean (the average income of all the prosecutors) will fall. b. What percentage of prosecutors earn \$60,000 or less in a year? c. What percentage of prosecutors earn between \$55,000 and \$65,000? d. What percentage of prosecutors earn more than \$65,000?

2. Researchers from the Legal Studies department conducted a study to examine factors that predict prosecutorial decision making among prosecutors in Mississippis lower courts. The aim of the study was to examine whether prosecutorial decision is influenced by extra-legal factors such race, gender, age, and ethnicity. The sample size was 50 selected randomly from the population of prosecutors in the lower courts. The main instrument for data collection was questionnaire. One question on the questionnaire asked how old are you? This question was used to measure age of the officers in the sample. Using a simple analysis, the following summary statistics were produced for this item (Age): Mean age was 40 years and a standard deviation of 5.00. Respond to the following:

a. Using 99% confidence level, determine the confidence interval within which the true population mean (the average age of all the prosecutors) will fall. b. What percentage of prosecutors were 45 years or younger? c. What percentage of officers were between 30 years and 45 years? d. What percentage of officers were above 45 years?

Note: For both scenarios, you must show all calculations leading to the final answers. Dont just put the final answers down for me. Also, you have to use the appropriate formula for calculating confidence intervals based on the sample size.