Explanation Calculation: The contingency table with 3 rows and 3 columns is given. The three rows consist of three different shifts and the three columns consist of three different qualities of Welds. Contingency table: A contingency table is obtained as using two qualitative variables. One of the qualitative variable is row variable that has one category for each row of the table another is column variable has one category for each column of the table. Step 1: The hypotheses are: Null Hypothesis: H 0 : The quality of Welds and shifts are independent . That is, the quality of Welds does not vary among shifts. Alternate Hypothesis: H 1 : The quality of Welds and shifts are not independent . That is, the quality of Welds varies among shifts. Step 2: Now, it is obtained that, Number of Welds High Quality Moderate Quality Low Quality Row Total Day Shift 467 191 42 700 Evening Shift 445 171 34 650 Night Shift 254 129 17 400 Column Total 1,166 491 93 1,750 Step 3: Expected frequencies: The expected frequencies in case of contingency table is obtained as, E = Row total ⋅ Coloumn total Grand total . Now, using the formula of expected frequency it is found that the expected frequency for the high quality Welds and the Day Shift is obtained as, ( 700 ) ( 1 , 166 ) 1 , 750 = 816 , 200 1 , 750 = 466.400 . Hence, in similar way the expected frequencies are obtained as, Number of Welds High Quality Moderate Quality Low Quality Day Shift ( 700 ) ( 1 , 166 ) 1 , 750 = 466.400 ( 700 ) ( 491 ) 1 , 750 = 196.40 ( 700 ) ( 93 ) 1 , 750 = 37.200 Evening Shift ( 650 ) ( 1 , 166 ) 1 , 750 = 433.086 ( 650 ) ( 491 ) 1 , 750 = 182.371 ( 650 ) ( 93 ) 1 , 750 = 34.543 Night Shift ( 400 ) ( 1 , 166 ) 1 , 750 = 266.514 ( 400 ) ( 491 ) 1 , 750 = 112.229 ( 400 ) ( 93 ) 1 , 750 = 21.257 Step 4: Level of significance: The level of significance is given as 0.01. Chi-Square statistic: The chi-square statistic is obtained as χ 2 = ∑ ( O − E ) 2 E where O 1 , O 2 ,

2nd Edition

ISBN: 9781259570643

Author: Navidi

Publisher: MCG

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Question

Chapter 10, Problem 9RE

To determine

Explain whether it is possible that the quality varies among shifts at the level of significance of α=0.01.

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