A psychologist would like to examine the effects of different testing methods on the final performance of college students. One group has regular quizzes (n=4), one group has three large exams (n=4), and the third group only has a final exam (n=4). At the end of the course, the psychologist interviews each student to get a measure of the student’s overall knowledge of the material. Quizzes Exams Final Only 4 1 0 N = 12 6 4 2 G = 36 3 5 0 ΣX2 = 164 7 2 2 T = 20 T = 12 T = 4 SS = 10 SS = 10 SS = 4 1. What are the null and alternative hypotheses? 2. Compute SStotal SSbetween and SSwithin 3. Compute dftotal, dfbetween, and dfwithin 4. Compute the variance between treatments (MS Between) and variance within treatments (MS Within) 5. What is the F-ratio? 6. Using the F-Distribution table, find the critical value for a hypothesis test where α = .05. 7. Should the researcher reject the null hypothesis? Why or why not? 8. Should the researcher do any follow-up testing? Why or why not?
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!
Quizzes Exams Final Only
4 1 0 N = 12
6 4 2 G = 36
3 5 0 ΣX2 = 164
7 2 2
T = 20 T = 12 T = 4
SS = 10 SS = 10 SS = 4
1. What are the null and alternative hypotheses?
2. Compute SStotal SSbetween and SSwithin
3. Compute dftotal, dfbetween, and dfwithin
4. Compute the variance between treatments (MS Between) and variance within treatments (MS Within)
5. What is the F-ratio?
6. Using the F-Distribution table, find the critical value for a hypothesis test where α = .05.
7. Should the researcher reject the null hypothesis? Why or why not?
8. Should the researcher do any follow-up testing? Why or why not?
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