You want to find out if developmental English courses had a positive affect on students' writing skills. You have a sample of 11 students do a writing sample the first day of class and on the last day of class. You want to determine if there is significant gains in writing ability at the 0.05 level. You believe the population of difference sc
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 had a positive affect on students' writing skills. You have a sample of 11 students do a writing sample the first day of class and on the last day of class. You want to determine if there is significant gains in writing ability at the 0.05 level.
You believe the population of difference scores is
| post-test | pre-test |
|---|---|
| 42.8 | 40.6 |
| 57.5 | 55.5 |
| 35.6 | 33 |
| 51.2 | 48.3 |
| 55.3 | 53.1 |
| 43.6 | 41.6 |
| 42.5 | 40.3 |
| 59.4 | 56.3 |
| 61.9 | 58.8 |
| 48.1 | 45.7 |
| 41.6 | 39.2 |
Use a 0.05 significance level.
What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =
What is the test statistic for this sample? (Use the Post - Pre column and report answer accurate to three decimal places.)
test statistic =
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