Question

1. Coil winding machines. A plant contains a large number of coil winding machines. A production analyst studied a certain characteristic of the wound coils produced by these machines by selecting four machines at random and then choosing 10 coils at random from the day's output of ench selected machines. The results follow. 1 2 3 1 205 204 207 2 201 204 198 3 198 204 196 4 210 209 214 4 5 6 202 208 206 203 209 207 201 199 203 215 211 208 7 209 199 202 210 8 9 10 205 207 206 206 205 204 198 202 197 209 211 210 Assume that ANOVA model Y; = Hitej (i.e., random cell means model) is appropriate. (a) Test whether or not the mean coil characteristic is the same for all ma- chines in the plant; use = 0.1. State the alternatives, decision rule, and conclusion. What is the P-value of the test? (b) Estimate om/(+ o) with a 90% confidence interval. Interpret your interval estimate. (c) Test whether or not and o- are equal: use a 0.1. State the alterna- tives, decision rule, and conclusion. (a) Estimate o? with a 90% confidence interval. Interpret your interval esti mate. (e) Obtain a point estimate of o..

Answer 1

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Some notations aret SSTO d.fanr df Ex-L MSTR SSTR SS TR nM Y- Sς E. EC) )_von on(.) 1iiECMSE) (i)ECHSTR- not Heuce noto Since Estimate of SnE MSTRMSE given y nd MSTRSMSF th 11 n Saik equnl to 2or0 ANOVA Table Sounce fh Cait windig machiay data 55 df Hachine 3 Erra n-ir= 36 Total nrl39 859-90 MS Pavalue 200. 83 Or0o00 254 40 ST.t N Hypotheaes Teing HyPatheacs: Ho o The Meava Value of the Chanacterstist of the Coikt ts the Same f every naachine Ha a20 The Mean Value af the chanactentic of the Coidts diffens betveen machines Decision Rule f FFELA1 3Ca- 2.24.26, then fail to neject to FXFEL-a Ca 24.26 then _neject Ho we get F-28 .092242 So There is Sigrnificant evidence to Conclusion we reject Ho Suggest that the mean chaactratic of the Coils ditfers behueu machines er p-Value 3,gO2 B665 X109 2019-11-11 06:07