Due Thursday October 20, 2011
Reading: October 11 – October 20
October 25 – November 1
Assignment:
Chapter 6
Chapter 7
1.
Complete the following problems from the text: 6.3, 6.4, 6.7, 6.8, 6.43, and 6.44.
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 P( x ) x P( x )
1 0.041 7 0.015
2 0.348 8 0.004
3 0.325 9 0.003
4 0.177 10 0.001
5 0.053 11 0.001
6 0.031 12 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.
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
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Diego conducted a study 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
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Roy and Christenfeld (2004), “Do Dogs Resemble their Owners?” Psychological Science , 15 (5), 361-
363.
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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. 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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