Stat 104 – Homework 7
Due Thursday October 24, 2013
Reading:
October 15 – October 24
October 29 – November 5
Chapter 6
Chapter 7
Assignment:
1. Complete the following problems from the text: 6.3, 6.7, and 6.43.
6.3 San Francisco Giants hitting
6.7 Which wager do you prefer?
6.43 Jury duty
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2. Students in an introductory statistics class at Iowa State University were asked: “How
many children, including yourself, are in your family?” A student is selected at
random from all the students who answered the question and let X = the number of
children in that students family. Below is the probability distribution for X.
x
1
2
3
4
5
6
P(x)
0.041
0.348
0.325
0.177
0.053
0.031
x
7
8
9
10
11
12
P(x)
0.015
0.004
0.003
0.001
0.001
0.001
a) How do you know that P(x) is a probability distribution?
b) What is the probability that a randomly selected student is an “only child”?
c) What is the most likely number of children in the family of a randomly selected
student?
d) What is the probability that a randomly selected student is from a family with 8 or
more children?
e) What is the mean number of children per family for students in this introductory
statistics class?
f) Consider the population of all families in Iowa. Would the mean number of
children per family in Iowa be close to the mean number you calculated in e)?
Explain briefly.
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3. 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 study1 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 randomly 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?
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Roy and Christenfeld (2004), “Do Dogs Resemble their Owners?” Psychological Science, 15 (5), 361363.
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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.
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 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.
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