Applying the Concepts and SkillsLosses to Robbery. Refer to Problem. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference in mean losses exists among the three types of robberies? Use one-way ANOVA to perform the required hypothesis test. (Note: T1 = 4899, T2 = 7013, T3 = 4567, and Σx2 = 16,683,857.)Losses to Robbery. The Federal Bureau of Investigation conducts surveys to obtain information on the value of losses from various types of robberies. Results of the surveys are published in Population-at-Risk Rates and Selected Crime Indicators. Independentsimple random samples of reports for three types of robberies— highway, gas station, and convenience store—gave the following data, in dollars, on value of losses. Highway Gasstation Conveniencetore 952 1298 844 996 1195 921 839 1174 880 1088 1113 706 1024 953 602 1280 614 a. What does MSTR measure?b. What does MSE measure?c. Suppose that you want to perform a one-way ANOVA to compare the mean losses among the three types of robberies. What conditions are necessary? How crucial are those conditions?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Applying the Concepts and Skills
Losses to Robbery. Refer to Problem. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference in mean losses exists among the three types of robberies? Use one-way ANOVA to perform the required hypothesis test. (Note: T1 = 4899, T2 = 7013, T3 = 4567, and Σx2 = 16,683,857.)
Losses to Robbery. The Federal Bureau of Investigation conducts surveys to obtain information on the value of losses from various types of robberies. Results of the surveys are published in Population-at-Risk Rates and Selected Crime Indicators. Independentsimple random samples of reports for three types of robberies— highway, gas station, and convenience store—gave the following data, in dollars, on value of losses.
| Highway | Gasstation | Conveniencetore |
| 952 | 1298 | 844 |
| 996 | 1195 | 921 |
| 839 | 1174 | 880 |
| 1088 | 1113 | 706 |
| 1024 | 953 | 602 |
| 1280 | 614 |
a. What does MSTR measure?
b. What does MSE measure?
c. Suppose that you want to perform a one-way ANOVA to compare the mean losses among the three types of robberies. What conditions are necessary? How crucial are those conditions?
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