(can someone please explain this to me in the most simplest and easiest way with step-by-step calculations of everything, I'm really having a hard time solving them or figuring out how to do it)

• When reporting numerical figures, please use two decimal places of accuracy.

Scenario:

You have been hired by a large technology company to conduct some research. The company is starting up a new manufacturing line, and is interested to know if the error rates in product manufacture can be reduced with training.

The new division has 17 front line workers, and these workers are randomly assigned to one of 3 training programs: on-the-job training (no formal training time), half-day training (4 hours in length), and full-day training (8 hours in length).

For each worker, the number of errors made in their first 200 hours of work (one month) is recorded.

Training Group	Error Rate
On-the Job	5.00
On-the Job	10.00
On-the Job	16.00
On-the Job	17.00
On-the Job	22.00
Half-Day	10.00
Half-Day	11.00
Half-Day	12.00
Half-Day	12.00
Half-Day	13.00
Half-Day	14.00
Full-Day	7.00
Full-Day	8.00
Full-Day	8.00
Full-Day	8.00
Full-Day	8.00
Full-Day	9.00

Questions:

You can use this ANOVA Source Table to help organize your results.

Source	SS	df	MS	F
Training (Between)		k - 1
Error (Within)		df1+ df2 + df3
Total		N - 1 16

1. State the null and alternate hypotheses for this study. [1 mark]
2. With the information provided, can we make an apriori hypotheses? If yes, what is this hypothesis. If no, explain why you can not do so. [1 mark]
3. Calculate the SS (Sum of Squares) for a) training, b) error, and c) total. [3 marks]
4. How many degrees of freedom are there: a) between groups, and b) within groups? [1 mark]
5. Calculate the values for a) MS_between and b) MS_within? [1 mark]
6. What is the final calculated value of F?[1 mark]
7. Assuming =0.05, what is the critical value of F for this study? [1 mark]
8. Does the calculated F-score reflect a significant difference? What does this finding tell us about the effect of training on error rates? [1 mark]
9. Calculate the Tukey HSD for this scenario. (NOTE: q = 3.70) [1 mark]
10. Which of the three training programs would you recommend that the company uses to train future employees at their manufacturing plants? Why would you recommend this program over others? (Use the statistics from Questions 8 & 9 to support your argument). [2 marks]

Final Challenge Question:

Assume that the workers are paid $20/hr during their training. Assume that each error made costs the company $5 of time and materials. If the company changes its product line every six months and a new training session is required for each product line, is your recommended training program still "worth it" for the company. Demonstrate the calculations you would use to determine this.