Consider an experiment to determine the effects of alcohol and marijuana on driving. Five randomly selected subjects are given alcohol to produce legal drunkenness and then are given a simulated driving test (scored from a top score of 10 to a bottom score of 0). Five different randomly selected subjects are given marijuana and then the same driving test. Finally, a control group of five subjects is tested for driving while sober. The driving test scores and the One-Way ANOVA table for these data are shown below. Test the hypothesis that there is a difference among the means of the three groups at 1% significance level. Alcohol Drugs Control 3 2 8 4 6 7 2 4 8 1 4 5 3 3 6 The following is the summary statistics for the table above generated from an Excel one-way ANOVA analysis: ANOVA SS df MS F P-value Between Groups 46.800 2 23.400 13.500 0.000848594 Within Groups 20.800 12 1.733 Total 67.600 14 Based on the Excel output, does there appear to be a difference between the means of the three groups at a 1% significance level? Let Group 1 = Alcohol, Group 2 = Drugs and Group 3 = Control so that: μ1= mean for the Alcohol group μ2= mean for the Drugs group μ3= mean for the Control group round your answer to 5 decimal places. 1. What is the test P-value that should be used in your hypothesis test?
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.
Consider an experiment to determine the effects of alcohol and marijuana on driving. Five randomly selected subjects are given alcohol to produce legal drunkenness and then are given a simulated driving test (scored from a top score of 10 to a bottom score of 0). Five different randomly selected subjects are given marijuana and then the same driving test. Finally, a control group of five subjects is tested for driving while sober. The driving test scores and the One-Way ANOVA table for these data are shown below. Test the hypothesis that there is a difference among the means of the three groups at 1% significance level.
| Alcohol | Drugs | Control |
| 3 | 2 | 8 |
| 4 | 6 | 7 |
| 2 | 4 | 8 |
| 1 | 4 | 5 |
| 3 | 3 | 6 |
The following is the summary statistics for the table above generated from an Excel one-way ANOVA analysis:
| ANOVA | |||||
|---|---|---|---|---|---|
| SS | df | MS | F | P-value | |
| Between Groups | 46.800 | 2 | 23.400 | 13.500 | 0.000848594 |
| Within Groups | 20.800 | 12 | 1.733 | ||
| Total | 67.600 | 14 |
Based on the Excel output, does there appear to be a difference between the means of the three groups at a 1% significance level?
Let Group 1 = Alcohol, Group 2 = Drugs and Group 3 = Control so that:
- μ1= mean for the Alcohol group
- μ2= mean for the Drugs group
- μ3= mean for the Control group
round your answer to 5 decimal places.
1. What is the test P-value that should be used in your hypothesis test?
2. Compute 99% Bonferroni simultaneous confidence interval for each possible pair of treatments for multiple comparisons. Report the interval (rounded to 2 decimal places) for each pair.
Compare Alcohol versus Drugs: ____<μ1-μ2< _____
Compare Alcohol versus Contorl: ____<μ1-μ3< _____
Compare Drugs versus Control: ____<μ2-μ3< _______
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