exam2solution - Stat-312 Mid-term Exam Two Instructor: Lie...

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Stat-312 Mid-term Exam TwoInstructor: Lie XiongData: 11/13/14 Time Limit: 75 MinutesName (Print):This exam contains 7 pages (including this cover page) and 6 problems. Check to see if any pagesare missing. Enter all requested information on the top of this page. You are required to show allrelevant formulas and work on each problem in this exam.Percentiles may be useful for your calculation:z0.01= 2.33,z0.05= 1.64,z0.1= 1.28t0.05,6= 1.94,t0.05,7= 1.89,t0.05,8= 1.86,t0.05,9= 1.83,Pr(t8>0.528) = 0.306Cumulative Binomial Probabilities:Table 1:Pr(Xx) =xy=1b(y;n, p), n=15p0.500.6000.0000.00010.0000.00020.0040.00030.0180.00240.0590.00950.1510.03460.3040.095x70.5000.21380.6960.39090.8490.597100.9410.783110.9820.909120.9960.973131.0000.995141.0001.000
Stat-312Mid-term Exam Two - Page 2 of 711/13/141. (6 points) In a study of certain machinery device,nsuch devices were randomly selected andtheir weights (in kilogram) were recorded. The recorded weights are used to estimate true meanweightμ. Suppose that the device weight follows a normal distribution with unknown meanμand varianceσ2= 4. Consider hypothesesH0:μ= 10 vsHa:μ <10. Consider 0.01 leveltest.(a) (1 point) Write down the formula for test statistic.
(b) (2 points) Find the rejection region.
(c) (3 points) How many devices need to be selected so that the 0.01 level test hasβ(9) = 0.10(The probability of type II error atμ= 9)?
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Stat-312Mid-term Exam Two - Page 3 of 711/13/14

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Term
Fall
Professor
Chung
Tags
Statistics, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, rejection region, Zobs

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