Data 1

The Greenland company was conducting research to compare the proficiency of three training programs, Green 1, Green 2, and Green 3, in training assemblers of a piece of agricultural equipment. Twenty-one employees were randomly picked to the three programs. After completion of the programs, each person was required to assemble pieces of the equipment, and the average length of time required to complete the assembly was recorded. The results are shown in tables below ("?" represents missing value). (Note: IN ORDER TO GET FULL MARKS, SHOW ALL CALCULATION STEPS. FAILURE TO DO SO WILL RESULT IN A SCORE OF "0".) Average Variance Standard deviation Sum (Ex) Sample size Green 1 ? 59.8065 7.7335 195.5 ? Green 2 6.7188 ? 2.7853 53.75 8 Green 3 24.9583 111.0104 10.5361 149.75 6 a) Can Greenland company's manager infer at the 97.5% confidence level that there are differences in the average assembly times for people trained by the three programs? (Assume normal distributions with equal variances.) b) Estimate with 10% significance level the differences in mean assembly times between persons trained by programs Green 1 and Green 3. (Assume normal distributions with equal variances.)