The Pinball project is a designed experiment to determine the effect of different types of ball on the distance in which the ball is thrown. After gathering the data from thrown balls, a hypothesis test was done on the sample mean of each treatment (thrown ball) in a completely randomized design with an alpha around 0.05.

There are four discrete settings for both of the Pin Elevation and Bungee Position, numbered from the bottom up.
The Release Angle is a continuous variable from 90 to 180 degrees. And there are additionally three types of balls were used in the experiment.

The Pin Elevation and Bungee Position were both set at their fourth setting, i.e. highest setting.
The Release Angle was at 90 degrees, with the arm pulled fully back before releasing. The experiment comprised of 2 parts,

Part 1

a) Determine how many samples should be collected to detect a mean difference with a medium effect (i.e. 50% of the standard deviation) and a pattern of maximum variability with a probability of 75%.
b) Propose a layout using the number of samples from part (a) with randomized run order c) Collect data and record observations on layout proposed in part (b) d) Perform hypothesis test and check residuals, comment and take corrective action if necessary. e) If the null hypothesis is rejected, investigate pairwise comparisons.
f) State all findings and make recommendation.

Part 2

Perform a designed experiment to determine the effect of Pin Elevation and Release Angle on distance in which a red ball is thrown when the Bungee Position is fixed at the second position.
Settings one and three of Pin Elevation should be investigated as a fixed effect, as well as settings of the Release Angle corresponding to 110, 140, and 170 degrees as a random effect.
The design should be replicated three times.

a) State model equation with the null and alternative hypotheses to be tested. In addition, state the level of significance that was used in the analysis.
b) Propose a layout with a randomized run order c) Collect data and record observations on the layout proposed in part (a) d) Test the hypotheses and state conclusions, determining those effects that are significant. Generate plots that might be useful/necessary to show your findings. You may also show residual plots and make appropriate comments, but do not transform the data (i.e. use the raw data regardless of normality and variance constancy)