At the 0.10 significance level, are the meancompletion times differ by students?
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.
A task requires the completion of four activities. A teacher would like to know if differences in the sequence of the four activities results in different task completion times. The teacher selects three students and demonstrates the activities in random order to the students. Then each student completes the task with each of the activity sequences. The completion times are recorded. The following table shows the minutes for each student to complete each task. Assume that the populations from which the sample drawn are
| Ayşe | Sema | Ahmet | |
| A | 21 | 20.1 | 21.4 |
| B | 17.6 | 18.7 | 21.4 |
| C | 20 | 20.1 | 22.1 |
| D | 21.3 | 18.8 | 20.5 |
- 1. Complete the following analysis of variance table.
|
Source of Variation |
SS |
Df |
MS |
F-Ratio |
|
Between Groups (Students) G |
Answer |
Answer |
Answer |
Answer |
|
Between Blocks (Activities) B |
4.83 |
Answer |
Answer |
Answer |
|
Error |
6.74 |
Answer |
Answer |
|
|
Total |
Answer |
Answer |
|
|
- At the 0.10 significance level, are the meancompletion times differ by students?
- a) NullHypothesis is
Ho:
Ho: Mean completion times for different students are equal
- b) Alternative Hypothesis is
H1: Mean completion times for different students are equal for at least one pair
H1: Mean completion times for different students are not equal for at least one pair
- c) F-Ratio isAnswer
- d) Critical Value of the test ata=10% is Answer
- e) Does it appear ata=10% that population completion times among students are different ?
May be
Yes for at least one pair
No
- At the 0.10 significance level, are the mean completion times differ by activity sequence?
- a) Null Hypothesis is
Ho: Mean completion times for different activity sequence are not equal
Ho: Mean completion times for different activity sequence are equal
- b) Alternative Hypothesis is
H1: Mean completion times for different activity sequence are equal for at least one pair
H1: Mean completion times for different activity sequence are not equal for at least one pair
- c) F-Ratio isAnswer
- d) Critical Value of the test at α=10% isAnswer
- e) Does it appear at α=10% that population means are different ?
May be
Yes for at least one pair
No
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