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## E-Book Chapter Eight 8.46 Solutions

by: smartwriter Notetaker

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# E-Book Chapter Eight 8.46 Solutions

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smartwriter Notetaker
CSU - Dominguez hills
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E-Book Chapter Eight 8.46 Solutions
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KARMA
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Date Created: 11/15/15
846 A random sample of 10 miniature Tootsie Rolls was taken from a bag Each piece was weighed on a very accurate scale The results in grams were 3087 3131 3241 3241 3270 3353 3400 3411 3437 3477 a Construct a 90 percent confidence interval for the true mean weight 2 make the con dence interval we need the standard deviation sample 2 2 mean observed 0 0 13199 n 10 x Z 3 3048 All the other info is of no use with a con dence interval 013199 1 72 71 0 x u x u o 013199 17 71 0 This is the test statistic 2 here we can derive the confidence interval We will make a 90 confidence interval 164ss s1645 013199 M 013199 11 0 013199 11 0 Zxbar 1645 Sprbar1645 013199 013199 z xbar l645 m xbarl645 m x Z33048 013199 013199 z xbar l645 W xbarl645 m 013199 013199 z 33048 1645 33048 1645 m l m z 32361395053373460495 i 00686604952 z 323337Jr 007 The 90 con dence interval of the true mean is 323 337 This is using the z confidence interval Although we want to using the t test since nlt30 SO now let s do the t confidence interval I NQ re 02013199 10 n x Z 33048 0 013199 511 0 We need 2 know the t value Since we are calculating the 90 con dence interval on 01 g 005 So tom on this t1 Signi cance level D De nes 2121112111 1111112111 1122111221 1121112111 111112111 221112111 Freed 1112121151 11212121121 11212121121 1112121121 21112121121 2111212121 1 22 221 21 221 12122 2214 2212 1 1122 2 2222 2222 4222 2222 1 2 212 2 2241 4241 2122 2222 1222 122 4 42114 2141 2112 2122 1 222 141 2 41122 2222 251 21112 1 412 121 2 2121 2142 2441 1 242 1 442 112 1 22211 2222 2222 1 2 1 412 111 2 2222 22 2222 2 1221 122 2 2222 2221 2222 mm 1 222 122 111 2122 2124 2222 1 212 1 212 1211 11 21112 2112 22111 1122 1222 221 12 21124 21 2112 1 122 1 222 222 12 21112 22211 2122 1111 12211 224 14 2211 2222 2142 1 121 1 242 222 12 2241 22112 2122 1 122 1 241 221 12 2221 2224 21211 1 142 1 221 2211 11 22 2221 21111 1 1411 1 222 2 12 2212 2222 2121 1 124 1 222 25 12 2221 2242 2222 1 122 1 222 em 21 2242 2222 21122 1 122 1 222 221 21 2221 2212 211211 1 121 1 222 222 22 2212 2222 21114 1 111 1 221 222 22 22111 22211 21122 1 114 1 222 222 24 2121 2422 21124 1 11 1 1 212 222 22 2212 2422 21122 1 122 1 212 224 22 2112 2412 21122 1 122 1 212 224 21 2111 2412 21122 1 1112 1 214 224 22 2122 2421 2242 1 121 1 212 222 22 2122 2422 2242 1 2 1 21 1 222 Large 252 2221 1 222 1 242 1 222 212 33048 1833 013199 lt lt3 30481833 013199 39 39 m U 2 33048 0076507489330480076507489 z 32282925913381307409 i 00765074089 z3228333813 00765 Notice the z t intervals do n It vary by much The 90 confidence interval of the true mean is about 32283 33813 b What sample size would be necessary to estimate the true weight with an error of i 003 grams with 90 percent con dence 0 013199 n10 x Z 33048 Margin of errorE 003 We wantZ have 90 confidence so CL 01 Z a 005 N Z005 1645 according Z the table So we can calculate now 2 Sampled Z 2 N 0Z E 6 013199 x1645 2 003 6 21712355 2 003 Z72374516672 35238070663 Y on always want 2 round up so the sample 2 would be 53 people The sample 2 be 53 c Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture Data are from a project by MBA student Henry Scussel Temperature consistency of batches machine tolerances There are so many variables that come to play The temperature in which the tootsie rolls are made could cause a variation in their weight the consistency of the batches how many tootsie rolls are made for each batch will also play an important role in determining the weight of the tootsie rolls and the machine tolerance how many tootsie rolls can each machine make before it has to shut down or cool down All of them combined make the variation of the weight

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