Problem 2 (Continuous Distribution)
A National Fear of Crime Victimization Survey is distributed every 5 years in the United States.
The survey is scored on a continuous scale (0-90). Lower scores indicate less fear of crime
victimization, higher scores indicate more fear of crime victimization. In 2013 the mean fear of
crime victimization score was 42. The survey was distributed again in 2018, and the mean was
found to be 63. Has the fear of crime increased in this country in the last 5 years? A researcher
takes a sample of 5,000 surveys to test this hypothesis.
• Null Hypothesis: The 2018 fear of crime victimization mean is equal to 42.
• Alternative Hypothesis: The 2018 fear of crime victimization mean is greater than 42.
• Alpha level =.05
• Z statistic critical value = 1.96
Decision rule: If the Z observed value is greater than 1.96, reject the null hypothesis, if
the Z observed value is not greater than 1.96, fail to reject the null hypothesis.
? Z observed value = 1.58
A. What type of tailed test is this?
B. What is the hypothesis decision (Reject the null hypothesis or Fail to Reject the null
hypothesis)?
C. Complete the following interpretation bullet points:
• Is this finding statistically significant?
• What is our formal conclusion/what does this mean?
• What is the chance of error (type and percentage)?
