Use the 0.05 alpha level. What is the critical value for this test? critical value = ±± What is the test statistic for this sample? test statistic = The test statistic is... not in the critical region in the critical region This test statistic leads to a decision to... fail to reject the null reject the null accept the null As such, the final conclusion is that... You were able to show that students had significant losses in writing ability at the end of the course You were able to show that their pre-course writing ability equaled their post course writing ability. You were unable to show any significant gains or losses in writing ability. You were able to show that students had significant gains in writing ability at the end of the course You were able to show that students had at least as good writing ability at the end of the course as they did in the beginning of the course
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
You want to find out if developmental English courses have ANY affect on students' writing skills. You have a sample 31 students do a writing sample the first day and on the last day of class. You want to determine if there is any significant gains or losses in writing ability at the 0.05 level.
You believe the population of difference scores is
| post-test | pre-test |
|---|---|
| 71.9 | 70.7 |
| 59.6 | 39.3 |
| 63.6 | 82.5 |
| 36.9 | 37.3 |
| 50.4 | 50.4 |
| 70.2 | 63.7 |
| 60.8 | 52.6 |
| 81.7 | 92.8 |
| 61.2 | 37.4 |
| 47.3 | 32 |
| 91.9 | 60.5 |
| 30.7 | 37.2 |
| 45.9 | 36.5 |
| 66.7 | 45.1 |
| 87.8 | 99.6 |
| 44.9 | 40.8 |
| 56.6 | 79.9 |
| 42.7 | 35 |
| 80.3 | 59.4 |
| 36.9 | 57 |
| 54.7 | 35.7 |
| 37.8 | 42.8 |
| 30.7 | 33.3 |
| 43.8 | 39.7 |
| 64 | 55.8 |
| 41.5 | 39 |
| 42.7 | 42.7 |
| 58.5 | 37.6 |
| 60.4 | 56.3 |
| 47.8 | 67.9 |
| 52.8 | 54.1 |
Use the 0.05 alpha level.
What is the critical value for this test?
critical value = ±±
What is the test statistic for this sample?
test statistic =
The test statistic is...
- not in the critical region
- in the critical region
This test statistic leads to a decision to...
- fail to reject the null
- reject the null
- accept the null
As such, the final conclusion is that...
- You were able to show that students had significant losses in writing ability at the end of the course
- You were able to show that their pre-course writing ability equaled their post course writing ability.
- You were unable to show any significant gains or losses in writing ability.
- You were able to show that students had significant gains in writing ability at the end of the course
- You were able to show that students had at least as good writing ability at the end of the course as they did in the beginning of the course
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