Is there a relation between murder and arson? A random sample of 15 Midwest cities (over 10,000 population) gave the following information about annual number of murder and arson cases. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.) City 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Murder 18 11 19 9 23 12 17 16 24 21 13 5 22 10 15 Arson 127 95 87 31 130 33 158 22 168 139 52 37 133 48 50 Use a 1% level of significance to test the claim that there is a monotone-increasing relationship between the ranks of murder and arson. (a) Rank-order murder using 1 as the largest data value. Also rank-order arson using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test. City Murder Rank x Arson Rank y d = x - y d2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Σd2 = (b) What is the level of significance? (c) Compute the sample test statistic. (Use 3 decimal places.)
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.
Is there a relation between murder and arson? A random sample of 15 Midwest cities (over 10,000 population) gave the following information about annual number of murder and arson cases. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.)
| City | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Murder | 18 | 11 | 19 | 9 | 23 | 12 | 17 | 16 | 24 | 21 | 13 | 5 | 22 | 10 | 15 |
| Arson | 127 | 95 | 87 | 31 | 130 | 33 | 158 | 22 | 168 | 139 | 52 | 37 | 133 | 48 | 50 |
Use a 1% level of significance to test the claim that there is a monotone-increasing relationship between the ranks of murder and arson.
| City | Murder Rank x |
Arson Rank y |
d = x - y | d2 |
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
Σd2 = |
(b) What is the level of significance?
(c) Compute the sample test statistic. (Use 3 decimal places.)
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