Stat 104 – Homework 6
Due Thursday October 28, 2010
October 12 – October 21
October 26 – November 2
Reading:
Chapter 6
Chapter 7
Assignment:
1. Complete the following problems from the text: 6.3, 6.4, 6.7, 6.8, 6.23, 6.24, 6.27,
6.28, 6.43, and 6.44.
2. Have you ever noticed that some dogs seem to look like their owners? Michael
Roy and Nicholas Christenfeld, Psychology professors at the University of
California San Diego conducted a study 1 to see if people could match a dog with
its owner. Pictures of 25 purebred dogs and separate pictures of their owners
were taken at dog parks in Southern California. The pictures were taken so that
the backgrounds were different for the dog and its owner. Study participants were
shown three pictures, one of the owner and two of dogs. One of the dog pictures
was actually that of the owner’s dog and the other was of another random selected
dog from the study. Study participants were asked to indicate which of the two
dogs most resembled the owner. Of the 25 owners of purebred dogs, 16 were
matched with the correct dog. If dogs don’t resemble their owners then the
probability that an owner is matched with the correct dog is 0.5 (participants are
guessing). It is reasonable to assume that matching one dog to one owner is
independent of matching another dog to another owner.
a) Was this study an observational study or and experiment? Explain briefly.
b) Use JMP to calculate the probability distribution for the number of correct
matches for the set of 25 owners of purebred dogs. Have JMP round
probabilities to 4 decimal places.
c) Have JMP create a histogram of the probability distribution. Be sure the
histogram has a probability axis.
d) Describe the shape of the probability distribution.
e) What is the probability that there are exactly 16 owners are matched with
the correct dog?
f) What is the probability that 16 or more owners are matched with the
correct dog?
g) What is the probability that 10 or fewer owners are matched with the
correct dog?
h) What is the probability that 10 or fewer owners are matched with the
incorrect dog?
i) What is the mean number of owners matched with the correct dog, round
to 1 decimal place? Explain how the mean number can be a fraction, even
though the number of correct matches is a whole number.
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Roy and Christenfeld (2004), “Do Dogs Resemble their Owners?”, Psychological Science, 15 (5), 361363.
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j) What is the standard deviation of the number of owners matched with the
correct dog, round to 2 decimal places?
k) What is the probability that the number of number of owners matched with
the correct dog falls between the mean minus two standard deviations and
the mean plus two standard deviations?
l) Turn in the JMP data table that contains the binomial probabilities as well
as the JMP output summarizing the distribution.
3. In the first lab data on the weights of unopened Fun Size bags of M&Ms were
collected. In fall 2008, data on the weight of contents, just the M&Ms with no
bag, were collected. Below is a histogram of weights of contents of Fun Size
bags.
40
Count
60
20
15
16
17
18
19
20
21
22
Weight of Contents (g)
a) Describe the shape of the histogram. Why is it reasonable to use a normal
model for the distribution of the weight of contents for all Fun Size bags
of M&M’s?
b) Use a normal model with μ = 18.5 g, and σ = 1.25 g for the distribution of
weight of contents for Fun Size bags of M&M’s.
i. What is the probability that a Fun Size bag will have a weight of
contents less than 16 g?
ii. What is the probability that a Fun Size bag will have a weight of
contents greater than 22 g?
iii. What is the probability that a Fun Size bag will have a weight of
contents between 17 g and 20 g?
iv. We wish to label the Fun Size bag such that 97% of all Fun Size bags
will contain at least the labeled weight. What should the label weight
be?
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