(In addition Draw Hass Diagram for every Problem)
Problem 12.2 (See attached for data) (Use R Programming and send Codes for this problem) (Draw Hass Diagram as well)
Dental fillings made with gold can vary in hardness depending on how the
metal is treated prior to its placement in the tooth. Two factors are thought
to influence the hardness: the gold alloy and the condensation method. In
addition, some dentists doing the work are better at some types of fillings
than others.
Five dentists were selected at random. Each dentist prepares 24 fillings
(in random order), one for each of the combinations of method (three levels)
and alloy (eight levels). The fillings were then measured for hardness using
the Diamond Pyramid Hardness Number (big scores are better). The data
follow (from Xhonga 1971 via Brown 1975)
Analyze these data to determine which factors influence the response and
how they influence the response. (Hint: the dentist by method interaction
can use close inspection.)
Exercise 12.4 (Also Draw Hass Diagram)
Briefly describe the treatment structure you would choose for each of
the following situations. Describe the factors, the number of levels for each,
whether they are fixed or random, and which are crossed.
(a) One of the expenses in animal experiments is feeding the animals. A
company salesperson has made the claim that their new rat chow (35%
less expensive) is equivalent to the two standard chows on the market.
You wish to test this claim by measuring weight gain of rat pups on the
three chows. You have a population of 30 inbred, basically exchangeable female rat pups to work with, each with her own cage.
(d) The disposable diaper business is very competitive, with all manufacturers trying to get a leg up, as it were. You are a consumer testing
agency comparing the absorbency of two brands of “newborn” size
diapers. The test is to put a diaper on a female doll and pump bodytemperature water through the doll into the diaper at a fixed rate until
the diaper leaks. The response is the amount of liquid pumped before
leakage. We are primarily interested in brand differences, but we are
also interested in variability between individual diapers and between
batches of diapers (which we can only measure as between boxes of
diapers, since we do not know the actual manufacturing time or place
of the diapers). We can afford to buy 32 boxes of diapers and test 64
diapers.
Problem 12.5 (Also Draw Hass Diagram)
City hall wishes to learn about the rate of parking meter use. They choose eight downtown blocks at random (these are city blocks, not statistical blocks!), and on each block they choose five meters at random. Six weeks
are chosen randomly from the year, and the usage (money collected) on each
meter is measured every day (Monday through Sunday) for all the meters on
those weeks. Answer the below Standard five questions.
(a) Draw the Hasse diagram for this model.
(b) Determine the appropriate denominators for testing each term using the restricted model assumptions. 308 Nesting, Mixed Effects, and Expected Mean Squares
(c) Determine the expected mean squares for each term using the restricted model assumptions.
(d) Determine the appropriate denominators for testing each term using the unrestricted model assumptions.
(e) Determine the expected mean squares for each term using the unrestricted model assumptions.
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