HW_Week6.docx - UMUC STAT-200 Homework Assignments Dr Brian...

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UMUC STAT-200 Homework Assignments Week #6 Dr. Brian Killough Textbook #1: Lane et al . Introduction to Statistics, David M. Lane et al., 2013. ( http://onlinestatbook.com/Online_Statistics_Education.pdf ) Textbook #2: Illowsky et al . Introductory Statistics, Barbara Illowsky et al., 2013. ( http://openstaxcollege.org/files/textbook_version/hi_res_pdf/15/col11562-op.pdf ) See the file named “UMUC_STAT200_EXCEL_Tips” at the “Course Materials” menu link to find functions for calculating the Normal Distribution and Student’s T-distribution values needed for this assignment. Lane - Chapter 11: (18) 18. You choose an alpha level of .01 and then analyze your data. a. What is the probability that you will make a Type I error given that the null hypothesis is true? “α is the probability of a Type I error given that the null hypothesis is true”, and in this example α=0.01 b. What is the probability that you will make a Type I error given that the null hypothesis is false? If the null hypothesis is false, then it is impossible to make a Type I error, therefore the probability = 0 Lane – Chapter 12: (7,13) 7. Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data in the table below. a. Compute L (linear effect of trial) for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject. Make a new column in your table with this result. a b c L 4 6 7 (-1)(4)+(0)(6)+(1)(7) = 3 3 7 8 (-1)(3)+(0)(7)+(1)(8) = 5 2 8 5 (-1)(2)+(0)(8)+(1)(5) = 3 1 4 7 (-1)(1)+(0)(4)+(1)(7) = 6 4 6 9 (-1)(4)+(0)(6)+(1)(9) = 5 2 4 2 (-1)(2)+(0)(4)+(1)(2) = 0 b. Compute a one-sample t-test on this column (with the L values for each subject) you created. HINT: See the example in the “Specific Comparisons” section of Chapter-12. Find the “t-value” and the “two-tailed probability” using the EXCEL “TDIST” function. Assume the statistic for this problem is “L” and use the following formula for the t-value. Also assume the hypothesized value is 0, since the contrast weighting (-1,0,+1) for a “perfect” set of data would make “L” be 0 in all cases. Stdv of L = 2.16 Mean of L (statistic) = 3.67 Standard Error = 2.16/√6 = 0.882
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DOF = 6-1 = 5 T= (3.67 – 0)/(0.882) = 4.16 P= 0.0088 t = (statistic – hypothesized value) / (standard error of the statistic) t = (Mean of L – 0) / (Standard Error of L) t-value = t = ´ X s n X = Sample Mean S = Sample Standard Deviation N = Number of L-Samples 13. You are conducting a study to see if students do better when they study all at once or in intervals. One
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