Exam 1 - 1 ID# Exam 1 PS 217, Spring 2008 As always, the Skidmore Honor Code is in effect. Thus, as indicated in the cartoon below, no cheating of any kind will be tolerated. At the end of the exam, you’ll write the Honor Code and sign it to attest to your adherence. It’s very important that you show all your work, otherwise I won’t be able to give you partial credit, should you arrive at a wrong answer. Keep in mind that the point-value of a question is a cue to the time it should take you to answer the question. Thus, you shouldn’t work much more than 10 minutes on a 10-point question, otherwise you won’t finish the exam. Good Luck! 1. In class, we talked about the poor woman who was pregnant in San Diego. She argued that she had a very long gestation period (i.e., 308 days). Essentially, she is claiming that her gestation period was sampled from the normal population (µ = 268 days and σ = 16 days). When faced with a situation such as this, a statistician has to make a decision. Assuming that he couldn’t simply conduct a DNA test, if the husband approached you for statistical advice, what would you do and what would you tell him? What kind of error might you be making with your decision? Why is it that you can never make a Type I Error and a Type II Error on the same decision? [5 pts]Exam 1 - 2 2. If you think of IQ scores as normally distributed with µ = 100 and σ = 15, you should be able to answer the following questions: [3 pts each] a. What proportion of IQ scores would fall between 115 and 130? b. What proportion of IQ scores would fall below 90? c. If you wanted to consider yourself smarter than 95% of people, what IQ score would you need to earn? d. If you administered an IQ test to a random sample of n = 9 people, what is the probability that their mean IQ would be greater than 109? e. If you were about to take a random sample of n = 9 people and you wanted to estimate the mean IQ of the sample, you might expect that it should fall in the middle 95% of the distribution. Thus, their mean would likely fall between what two scores?Exam 1 - 3 3. The GPAs for a sample of nine students are seen below. Using these data, estimate the mean and variance of the parent population from which the sample was drawn. [10 pts] GPA GPA2 3.5 12.25 2.9 8.41 3.2 10.24 3.0 9.0 2.8 7.84 3.6 12.96 3.2 10.24 2.9 8.41 3.3 10.89 Sum 28.4 90.24 4. Educators often talk about grade inflation. Suppose that the mean GPA in 1950 was 2.4 (i.e., µ = 2.4). How likely is it that the sample above (problem #3) was drawn from a population with µ = 2.4? What might this evidence say about grade inflation? [10 pts]Exam 1 - 4 5. Miscellaneous Questions [10 pts]: a. Suppose that you are computing a t-test with tCrit = 1.96. What can you tell me about that t-distribution? b. If you are looking for a small effect (low d), what would you need in order to be able to reject H0? c. What is the definition of the median? d. If you were to add a constant to all the scores in a sample, what would happen to the sample variance? e. Why is the SS not a good measure of variability? f. Interpret the SPSS output below as completely as you can. (In other words, what is the statistic, what are the scores, how would you interpret the results, etc.) Extra credit: [From memory lab] What is the name of the first psychologist to study memory
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