The Declining Crime Rates: A Hypothesis-Driven Analysis

Abstract

Milestone 3: Inference Overview and Objectives The primary objective of this project will be to perform a few hypothesis tests, make inferences on the test statistics, and state null/alternative hypotheses. The techniques used in modern inferential research require software beyond our current means (SPSS, R, SAS); however, we are nonetheless able to observe a few examples that are illustrative of the research process. You will work with populations, samples, and proportions in these exercises. You’ll then determine whether to use a Z-statistic or T-statistic to determine whether to reject the null hypothesis, and you’ll also make connections between hypothesis testing and confidence intervals. You’ll have the opportunity to explore real-world datasets in the fields of criminal justice, equity, and surveying. With a firm knowledge of this statistical concept, you’ll possess the conceptual knowledge necessary to further pursue these techniques if they interest you. Part One: Crime Analysis from 2016-2017 National law enforcement noticed an overall decline in crimes among U.S. citizens. This data set records the number of crimes in each state and the percentage change from 2016 to 2017. Let’s suppose that leadership would like to conduct a hypothesis test at the 1% significance level that crime has decreased over time (by using total percent change). For this part, you should look at the total percent change column to run your test. Performing the Test Step 1: Write the null hypothesis/alternative hypotheses below. Determine the tail type. : Left-tail Step 2: Perform the Hypothesis Test in Excel using the Total Percent Change column. Fill out the cells indicated on the spreadsheet and determine whether to accept/reject the null hypothesis. Step 3: Find a 99% confidence interval for the percent change from 2016 to 2017 by filling out the cells in the Excel sheet. Analysis of Results What is the conclusion of the hypothesis test? The left-tailed hypothesis test yields a p-value of 0.008715 which is smaller than 0.01. In conclusion, there is enough evidence to reject the null hypothesis. Was your null hypothesis mean contained within your confidence interval? Does this agree with the results of your hypothesis test? The null hypothesis mean was not included within the confidence interval since the upper limit is smaller than 0. The results of the confidence interval agree with the results of the hypothesis test that we reject the null hypothesis for the test. We can conclude at 99% confidence level that based on the data, crime has decreased over time. Part Two: Gender Perception in the Workforce Gender perception in the workplace can often be skewed. For example, jobs in STEM can often be overrepresented by men, which can have negative consequences for budding female scientists. But how can we quantify the extent of this gender misperception? This data set is taken from the Pew Research Center, which used an algorithm to sample the proportion of women found in images that represent various occupations. They then compared this to the proportion of women who actually work in the field, taken from the Bureau of Labor Statistics (BLS). Suppose researchers want to show that women are underrepresented by more than 5% in STEM-related jobs at a 95% confidence level. Our data set then serves as a representative sample of all occupations and would give us a good look into whether women were accurately portrayed in images. Performing the Test Step 1: Write the null hypothesis/alternative hypotheses below. Determine the tail type. : Right-tailed Step 2 (SKIP. This is already done for you with the column labeled “Difference”): Find the difference between the true proportion of women who work in the field compared to the image search proportion for each occupation (bls_proportion_women) – (image_search_proportion_women). Step 3: Perform the Hypothesis Test in Excel using the ‘Difference’ column. Remember that you’re working with a...