Four different glazes are applied at two different thicknesses to clay pots. The kiln used in the glazing can hold eight pots at a time, and it takes 1 day to apply the glazes. The experimenter wanted eight replications of the experiment. Since conditions in the kiln vary somewhat from day to day, the experiment was conducted over an 8-day period. The experiment is conducted so that each combination of a thickness and type of glaze is randomly assigned to one pot in the kiln each day.                 Identify whether the design is a completely randomized design, randomized complete block design, or Latin square design. If there is a factorial structure for the treatments, specify whether it has a two-factor or three-factor structure. If the measurement units are different from the experimental units, identify both.

The iHub features an array of 3D printers for student use.  3D printers use plastic filament spools to print out plastic parts.  The iHub purchases 85% of their filament spools from Amazon, and the rest of their filament spools from Flash Forge.  It has been determined that 9% of the filament spools from Amazon are defective, while only 3% of the filament spools from Flash Forge are defective. i) The iHub randomly selects one filament spool from its inventory.  What is the probability of it being a defective filament spool?  (three decimals)     ii) If a filament spool at the iHub is randomly selected and determined to be defective, what is the probability that the filament spool was purchased from Amazon? (three decimals)

Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2," and were simply told the aim of the research was a "survey on dog–owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and…

A telemarketer is trying two different sales pitches to sell a carpetcleaning service. For Sales Pitch I, he contacted 175 people and 62 of these people bought the cleaning service. For Sales Pitch II, he contacted 154 people and 45 of these people bought the cleaning service. Does this indicate that there is any difference in the population proportions of the people who will buy the cleaning service, depending on which sales pitch he uses? Use α = 0.05.