A random sample of n, = 10 regions in New England gave the following violent crime rates (per million population). х 3.3 3.7 4.0 4.1 3.3 4.1 1.8 4.8 2.9 3.1 New England Crime Rate Another random sample of n, = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). X2: 3.5 4.3 4.5 5.3 3.3 4.8 Rocky Mountain Crime Rate 3.5 2.4 3.1 3.5 5.2 2.8
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference μ1 − μ2. Round the test statistic and critical value to three decimal places.)
| test statistic |
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