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practice2 - Statistics 101 Sample questions EXAM 2 1 A...

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Statistics 101 Sample questions: EXAM 2 1. A study was conducted of the effects of a special class designed to aid students with verbal skills. Each child was given a verbal skills test twice, both before and after completing a 4-week period in the class. Let Y = score on exam at time 2 - score on exam at time 1. Hence, if the population mean μ for Y is equal to 0, the class has no effect, on the average. For the four children in the study, the observed values of Y are 8-5=3, 10-3=7, 5-2=3, and 7-4=3 (e.g. for the first child, the scores were 5 on exam 1 and 8 on exam 2, so Y = 8-5=3). It is planned to test the null hypothesis of no effect against the alternative hypothesis that the effect is positive, based on the following results from a computer software package: Number Variable of Cases Mean Std. Dev. Std. Error Y 4 4.000 2.000 1.000 a. Set up the null and alternative hypotheses. b. Calculate the test statistic, and indicate whether the P-value was below 0.05, based on using the appropriate table. c. Make a decision, using α = .05. Interpret. d. If the decision in (c) is actually (unknown to us) incorrect, what type of error has been made? What could you do to reduce the chance of that type of error? e. True or false? When we make a decision using α = . 05, this means that if the special class is truly beneficial, there is only a 5% chance that we will conclude that it is not beneficial. 2. For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51 nonvegetarian students and a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students. a. Defining appropriate notation, state the null and alternative hypotheses for testing whether there is a difference between population mean ideology for vegetarian and nonvegetarian students. b. When we use software to compare the means with a significance test, we obtain the printout Variances T DF Prob>|T| --------------------------------------- Unequal 2.9146 41.9 0.006 1
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Interpret the P -value, in context, based on its definition. (Note: You are not being asked to make a decision at some α -level.) 3. A multiple-choice test question has four possible responses. The question is designed to be very difficult, with none of the four responses being obviously wrong, yet with only one correct answer. It first occurs on an exam taken by 400 students. The designers test whether more people answer the question correctly than would be expected just due to chance (i.e., if everyone randomly guessed the correct answer). a. Set up the hypotheses for the test. b. Of the 400 students, 125 correctly answer the question. Find the P -value, and interpret. c. Make a decision about H 0 , using α = . 05. Based on this decision, what can you conclude about the parameter?
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