random sample of 1000 daily newspapers found that on average, each edition contained 3.01 local crime stories per
day, with a standard deviation of 2.65. Answer the following questions assuming that the distribution of crime stories in newspapers is normal.
What is the Z score associated with a newspaper with 8 local crime stories?
What proportion of newspapers published five or fewer crime stories? How many does this correspond to in the sample?
What number of news stories corresponds to a Z score of +1?
What percentage of newspapers publish between 1 and 6 local crime stories per day?
7) Can the standard deviation of a variable ever be smaller than, or even equal to the standard error for the same variable? Justify your answer by means of both a formula and a discussion of the relationship between these two concepts.
8a) (Hypothetical) In a major national survey of crime victimization, the researchers found that 16.7% of Americans age 12 or older had been a victim of crime. The size of the sample was 144,400.
Estimate the percentage of Americans age 12 or older who were victims at the 95% confidence level. State in words the meaning of that result.
Estimate the percentage of victims at the 99% confidence level.
Imagine that the Sample size was cut in half but the survey found the same value of 16.7% for the percentage of victims.
By how much would the 95% confidence level increase?
By how much would the 99% confidence interval increase?
8b) (Hypothetical) You are conducting research on the prevalence of severe binge drinking among college students. You define severe binge drinking as consuming 10 or more alcoholic beverages at a single sitting. You ask the question: “On how many days in the past two weeks have you consumed ten or more drinks at one time? The answers can range from 0 to 14. You collect data on a sample of 900 students.
The average for this sample in 1.37 with a standard deviation of .80. Construct a 95% confidence interval for the average binge drinking score in the population. Another student who reviewed your figures, says your math is correct, but using the normal distribution isn’t correct because the binge drinking scores are highly skewed, with some students binging very frequently, and the majority of students never binge drinking at all. Is she correct that it is inappropriate to calculate a confidence interval for this research question?