Based on the Excel output, what conclusion can the researcher arrive?
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.
Suppose a researcher is interested determining whether on average, driving times on the major traffic routes are approximately the same. The following data are randomly collected from three major traffic routes.The entries in the table are drivings times in minutes on the these routes.
| Route 1 | Route 2 | Route 3 |
|---|---|---|
| 45 | 39 | 41 |
| 42 | 40 | 40 |
| 46 | 39 | 41 |
| 43 | 40 | 42 |
| 43 | 39 | 43 |
| 43 | 39 | 43 |
| 43 | 41 | 40 |
| 43 | 38 | 40 |
| 48 | 41 | 41 |
| 45 | 39 | 43 |
| 39 | 40 | |
| 39 | 40 | |
| 46 | 43 | |
| 40 | 41 | |
| 40 | 42 | |
| 40 | ||
| 40 | ||
| 46 | ||
| 46 | ||
| 41 |
A One-Way ANOVA test was conducted at a 0.02 level of significance. The results are shown below.
Note that some values in the table might be in scientific notation. Say, 1.65E-07 means 1.65x10-7 or 0.000000165.
ANOVA: Single Factor
| SUMMARY | ||||
|---|---|---|---|---|
| Groups | Count | Sum | Average | Variance |
| Route 1 | 10 | 441 | 44.100 | 3.433333 |
| Route 2 | 15 | 599 | 39.933 | 3.495238 |
| Route 3 | 20 | 833 | 41.650 | 3.502632 |
| ANOVA | ||||||
|---|---|---|---|---|---|---|
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 104.19444 | 2 | 52.09722 | 14.9476 | 0.00001 | 4.30012 |
| Within Groups | 146.38333 | 42 | 3.48532 | |||
| Total | 250.57778 | 44 |
Based on the Excel output, what conclusion can the researcher arrive?
- For 0.02 level of significance the ANOVA test shows the sample means and the sample variances, but fails to answer the question whether different traffic routes affect the average driving times. Probably, the researcher should increase the sample sizes.
- At the 0.02 level of significance, the sample data support the claim that there is a difference in the average driving times. On average,the driving times on the major traffic routes are not the same.
- For 0.02 level of significance the ANOVA test is unable to give positive or a negative answer to the question whether different traffic routes affect the average driving times. The question needs futher investigation.
- At the 0.02 level of significance,there is not sufficient sample evidence to support the claim that there is a difference in the average driving times. On average, the driving times are approximately the same.
- None of the above
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