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Unformatted text preview: Stat 3022 Data Analysis, Section 001 Midterm II, Nov 18, 2009 Print your name: Student Id No. Lab: You have 50 minutes to complete this exam. The exam is closed book. You may use a calculator
and one sheet of paper (size 8.5”X11”) with formulas or other notes on both sides. Please put all of your work on this test form (use the back if necessary). Table A and D are attached. The total is 50 points. This exam must be your own work entirely. Problem 1 [20 pts]: Suppose individuals with a certain gene have a 0.7 probability of eventually contracting a certain disease. Consider 60 individuals with the gene participate
in a lifetime study. a) [4 pts] Let X: the number of individuals who will contract the disease, what is the
distribution of X? (Specify the name of distribution and the values of parameters) X m _BihOMI\’liiéaz 0s?) b) [4pts] What is the mean and standard deviation of X? mam z/Mx 71? :60Xo.?=42 Sci :J n“Pu—F) : / goxmx 0.3 2 5.35” c) [6 pts] What is the chance that more than 50 individuals contract the disease? Use normal approximation and express the probability using standard normal distribution
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d) [6 pts] Consider ‘tge sample proportion, X/60, what is the approximate sampling
distribution for the sample proportion (including shape, mean, and standard error)? And justify your answer. (Do you use any theorem or assumptions? Are they
satisfied?) ‘h’F: +1215, n (I—r): 183’? 90 in“ QAWLW‘? MW (3.»: Maw: Mm, M?) u Problem 2 [15 pts]: We randomly select a group of 9 subjects from a population with a mean IQ of 100 and standard deviation of 15 @2100, o : 15). We give the subjects intensive
"Get Smart" training and then administer an IQ test. The sample mean IQ is 113. a) [8 pts} Did the training result in a significant increase in IQ score? i.e. Does training subjects
with the Get Smart training program, increase their IQ significantly over the average IQ for
the general population? ( Test H0: u=100 vs H1: u>100). Please use the significance level 0.10.
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ype e b) [2 pts] What is th rro of your test?
or: agnma Uzi/ext :th I W Z N c) [5 pts] Calculate the power of your test against the alternative 11 =110. Power :1 Fr (reject Ho (if Ha limit W) nzno
= Pr( I” 31m M MING) i}
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N Problem 3 [15 pts]: Samples of both surface soil and subsoil were taken from five randomly selected agricultural locations in a particular county. The soil samples were analyzed to
determine both surface pH and subsoil pH, resulting in the following summary table. _——— Let u] and u; denote the true average surface pH and that of the true average subsoil pH,
respectively. Let ud = liz ul. Assume that surface and subsoil pH values are normally distributed.
Please answer the following questions based on the attached computer output. (a) [10 points] Use a: 0.05 to test H0: ud = 0 versus Ha : ud > 0. Should a matched pair ttest or
a pooled t— test be used? Why? Explain. A mauled Pour % slumltl 66 used 5;an ‘ULQ PH mice; are (0%ch
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150.03%: (9.132 > 0.57
‘3‘ ‘fMl t0 reject Ho: (b) [5 points] ]Construct a 95% confidence interval for ad. ‘tsz CI : ,1} :t Murine = ﬂd 3W “x tow/5,4 > x<c(6.55,5.98,5.59,6.17.5.92) > y<c(6.78,6.14,5.58,5.91,6.10) > n<—5 > mean(x) [1] 6.042 > mean(y) [1] 6.102 ( To be continued on next page) > sd(x)
[1] 0.3526613 > sd(y)
[1] 0.4388850 > diff<yx > dbar<—mean(diff)
> dbar [1] 0.06 > s<sd(difD > S [1] 0.2003746 ...
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 Spring '10
 YanpingQu

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