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Unformatted text preview: 1. True of False Questions (30 points): ® F a) If the population mean is known, there is no reason to run a hypothesis test on he population mean. T ® b) The P—value is usually chosen before an experiment is conducted. Cf) F c) In conducting a hypothesis test, it is impossible to simultaneously make both a Type I error and
a Type II error. T @ d) The probability of a Type 11 error does not depend on the probability of a Type I error.
T G) e) While the normal distribution is symmetric, the t—Idistributions are slightly skewed.
CT) F f) The greater the (if, the closer the t—distributions are to the normal distribution. ('13 F g) If there is sufﬁcient evidence to reject a null hypothesis at the 5% level, then there is sufﬁcient
evidence4,to reject it at the 10% level. _ 'Pvabaua c 8.2, < i 070 T ® h) In a study of high school students, a positive correlation (r = 0.95) was found between hours
spent per week doing homework and scores 0n standardized achievement tests. We can conclude that doing homework helps prepare students for these tests from the data. T ® i) The sample correlation coefﬁcient for the following 10 pairs of data (1, 2), (2, 4), (3, 8), (4, 16),
(5, 32), (6, 64), (7', 128'), (8,256), (9, 512), (10, 1024) is approximately 1 because 3; = 23. C1") F j) When 7" z 0, there still can be strong relationship between the variables. 2. (15 points) A random sample of 26 offshore oil workers took part in a simulated escape exercise, and their times (see) to complete the escape are recorded. The sample mean is 370.69 sec and the sample
standard deviation is 24.36 sec. ‘ O (5621) Construct a 95% upper conﬁdence bound on the true average escape time. Interpret your bound. “=19 7—) woes—:2. 76‘, dSzilg ﬁ:i.708 x=?>‘loa.eai, 52249)(3 5g ﬁrsum; ,__, orLLSQaq Ex
dbl. «g x + f";— \ISY'L
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' 7 526 70.69 + 53% 8J6 ,t?) . 37 8. 85 I \ﬁWPVQﬁ‘mHoW: @ i—g m mmsmjwﬁm Wm . mum M as. was aw“?
QSCApparHMQ is. ie‘ss Hxavx 3‘15,%4_ SQL_ :5 Pvt5 b) Construct a 95% lower conﬁdence bound on the true average escape time: Interpret your bound.
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Wk, 1 370.6%  ES’A/‘Z 816 = IVQ/ZM 5472.53 3. (10 points) A study is to be conducted on the proportion of homeowners who own at least two TV sets. How large a sample is required if we wish to be 90% conﬁdent that the error in estimating this
quantity is within 315%? ‘ ‘Pi Ci“) Zak: [.6455 use. P: ‘ + 5‘3 l(oq—SX Q V0 WOW Ciceron. i
e—g— (‘ mgr maswe; (De/3 is [he i\  E Ii 4. (10 points) An investigator wishes to estimate the difference between population mean SATM
scores of incoming freshmen in the College of Engineering and in the College of Science at Purdue
University. The population standard deviations are both roughly 100 points and equal sample sizes are  to be selected. What value of the common sample size n will be necessary to estimate the difference to
within :I:10 points with 99% conﬁdence? ' Mm, divs : 9
32—40
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>'@¥O.05 2 @What is Alices 95% conﬁdence interval for the difference of the mean?
(50:534t, 1L134J) 7’ l b) What is Bobs 95% conﬁdence interval for the difference of the mean? (LﬁZWO) te.a7%® a c) Which SAS result is correct? Why?
Be b1 S . TheeLb W A0200 l taco/mpl‘es’ we"? received WW3, Q) Vbd) Using the correct SAS output, carry out a hypothesis test to determine whether the mean overall
distance for brand lzand brand 2 are different? Use or = 0.01.
r ‘1 , i) State the null and the alternative hypotheses \(jrs ‘ H01 «Aka'41:. HOLE ii) Calculate the test statistics based on the correct SAS result on previous page oilh e6” it XL "317. [04 6
2'“ ""4 ' 1: 9:1.
65'+ 5:: .o + {0.0%} 256
——: {AL [0 [O q) ﬁsiii) Calculate the p—value. Do you reject the null hypothesis?
pwvmua : 2x 0““ 2; 0,02 ‘7 Ool do molt W Ho iv) State your conclusion in terms of the problem. \S' \I" , ‘CA '_
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d,i$‘l—uhCe. bvmol 1L camel brand 1 owe. ‘l’\’\.L same od elfislet 9"?)‘5 ...
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 Spring '08
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 Statistics

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