Question

(1 point) Mechanical engineers are studying the influence of cam shape on the vibration produced at a given set of frequencies. An experiment is run in which the vibrations produced by four common cam shapes are measured and compared. Three specially made test cams are used. Each cam is divided into four sectors and each sector is machined to a different one of the four shapes. Thus all four shapes appear on each test cam. The test cams are run at a fixed speed and the displacement of a stylus riding on the cam is recorded. This signal is then broken into four signals corresponding to the four different cam- shape sectors. Each signal is broken into frequency components (called the spectrum) and the rms (root mean square) of the spectrum over a selected set of frequencies is computed. This value, which measures the amount of cam vibration at those frequencies, is the response variable. The data are displayed in table below Shape 1 Shape 2 Shape 3 Shape 4 52 39 60 Cam 162 Cam 2 66 Cam 3 76 Estimate the model effects 48 54. 47 60 81 T 1 T 2 βι β2 Въ Compute the ANOVA table (give the p-values to four decimal places) Source Shapes Cams df Sum of Squares Mean Square p-value ㄨㄨㄨㄨㄨ ㄨㄨㄨㄨㄨ Error Total ㄨㄨㄨㄨㄨ ㄨㄨㄨㄨㄨ Does the test reject the null hypothesis of equal mean vibration for all shapes at the 0.01 level? OA. Yes ○B.No

Answer 1

For Rows(cams) Null hypothesis Ho - Alternative hypothesis H1 14. 42.* 14, For Columns(shapes) Null hypothesis Ho :从1-4,-从,-从4 Alternative hypothesis H·4f从2 #从3 #从4 Grand Total-7-ΣΣ x-696 Raw sum of squares 2X-41992 Correction Factor (CF-2 40368 Total Sum of Squares (TSS)-ΣΣΧ2-CF-41992-40368-1624 Row Sum of Squares (RSS)-->,יד-CF, where be the square of ith row total Cormetion Fatr(C)696 N 3x4 2162+203 +2740368-780 4 -Σ7a-CF, where T be the square of (2042 +1802+1612+1512-40368 = Column Sum of Squares (C.SS)- column total j-1 544.6667 Error Sum of Squares (ES.S)-TS.S- RSS-C.S.S 1624- 780-544.6667298.8333 ANOVA table Source Rows(T)3-12 780 Columns (B) 4-1-3 544.6667 181.5556 Er (3-1)(4-1) 6 298.8333 49.8056 DF MS P-value a2 390 49.8056 7.8304E. -10.92 0.0500 (2.6) 181.5556 181 556 49 8056 3.6453-9.78 0.0499 (36) 12-1- 1624 Total The value of the test stati stic corresponding to cams (rows) is 7.8304 greater than the critical value Fas,-10.92 at 1% level of significance (2.6) P-value is equal to the level of significance We reject the null hypothesis corresponding to cams (rows) The value of the test statistic corresponding to shapes(columns) is 3.6453 less than the critical value Fan = 9.78 at 1% level of significance P-value less than the level of significance We fail to reject the null hypothesis corresponding to shapes (columns) Answer: B. No No, the test does not reject the null hypothesis of equal mean vibration for all shapes at the 0.01 level