5. The set of artificial data shown in Table 6.32 is used in severalcontexts to provide...

 

 

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5. The set of artificial data shown in Table 6.32 is used in severalcontexts to provide practice in implementing appropriate analyses for different situations. The use of the same numeric values for the different problems will save computational effort. Table 6.32 Data for Exercise 5 Treatment 1 2 5 11.6 8.5 14.5 12.3 13.9 10.0 9.7 14.5 12.9 16.1 10.5 6.7 13.3 11.4 14.3 10.6 7.5 14.8 12.4 13.7 10.7 6.7 14.4 11.6 14.9 (a) Assume that the data represent test scores of samples of students in each of five classes taught by five different instructors. We want to reward instruc- tors whose students have higher test scores. Do the sample results provide evidence to reward one or more of these instructors? 5. The set of artificial data shown in Table 6.32 is used in severalcontexts to provide practice in implementing appropriate analyses for different situations. The use of the same numeric values for the different problems will save computational effort. Table 6.32 Data for Exercise 5 Treatment 1 2 5 11.6 8.5 14.5 12.3 13.9 10.0 9.7 14.5 12.9 16.1 10.5 6.7 13.3 11.4 14.3 10.6 7.5 14.8 12.4 13.7 10.7 6.7 14.4 11.6 14.9 (a) Assume that the data represent test scores of samples of students in each of five classes taught by five different instructors. We want to reward instruc- tors whose students have higher test scores. Do the sample results provide evidence to reward one or more of these instructors?

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Statistical evaluation Null hypothesis Ho There is no significance difference between the Instructors teaching performance Alternative hypothesis Ha There is a significance difference between the Instructors teaching performance A B C D E 116 85 145 123 139 10 97 145 129 161 105 67 133 114 143 106 75 148 124 137 107 67 144 116 149 Statistical tool oneway analysis of variance abbreviated oneway ANOVA is a technique that can be used to compare means of two or more samples using Fdistributions Assumptions of ANOVA are following a The observations are independent b The parent population from which the sample observations are taken is Normal c Various treatments and environment effects are in additive nature Computer output SUMMARY Groups Count Sum Average Variance 116 4 418 1045 0096667 85 4 306 765 201 145 4 57 1425 043 123 4 483 12075 0489167 139 4 59 1475 105 ANOVA Source of Variation SS df MS F Pvalue F crit Between Groups 135278 4 338195 4148783 610E08 3055568 Within Groups 122275 15 0815167 Total 1475055 19 If F Calculated value less than F critical value than reject Null hypothesis ie 4148 305 reject the null hypothesis Therefore there is a significant difference between the Instructors teaching performance The above Anova Results and the box plot graph explain that there is a significant difference between the Instructors teaching performance If you observe that the variance between students to students score is low and the average score of students high for the instructor C whereas the variance between students to students score is slightly high for Instructor ... View the full answer