Assignment 5 solution (un-starred)

# Assignment 5 solution (un-starred) - THE UNIVERSITY OF HONG...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT0301 Elementary Statistical Methods Semester 1 2009/2010 Assignment 5 solution (un-starred) 2(a) Given σ = 8 and ߪ ௫ҧ ൌ2 , We know by Normal Sampling Theorem: ߪ ௫ҧ √௡ , Therefore, the minimum sample size needed is: ݊ൌቀ ൌቀ ൌ16 . Thus, the minimum amount needed is \$230 ൈ 16 ൌ \$3680. 2(b) There are typos in the Question, sample size should be 49 not 39 and ࢻ ൌ ૙. ૙૚ ࢔࢕࢚ ૙. ૙૞ .

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4(a) Let n be the size of sample. ݊൒ ቈ ݖ ଴.ଵ ߪ ܧ ൌ൤ 1.645 ൈ 160 45 ൌ 34.21 ݊൒35 Therefore, the minimum sample size required to supply this information is 35. 4(b) Let X = the boiling point of a particular liquid (in degrees C) X ~ N ሺߤ, ߪ ݊ൌ8 ,ݔҧ ൌ 139.75, ݏ ൌ 1.1250, ߙ ൌ 0.02, ݂݀ ൌ ݊ െ 1 ൌ 7. ݈݋݋݇ ݑ݌ 2 െ ݏ݅݀݁݀ ݐሺ7ሻ ଴.଴ଶ ൌ 2.998 Hence, 98% C.I. for ߤ : ݔҧേݐ ௡ିଵ · ݏ √݊ ൌ 139.75 േ 2.998 · 1.125 √8 ൌ ሺ138.5576,140.9424ሻ 6(a) Read example Class 11 question 5(a).

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## This note was uploaded on 04/14/2010 for the course STAT 0301 taught by Professor Gabriell during the Spring '09 term at HKU.

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Assignment 5 solution (un-starred) - THE UNIVERSITY OF HONG...

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