When choosing an item from a group, researchers have shown that an important factor influencing choice is the item's location. This occurs in varied situations such as shelf positions when shopping, filling out a questionnaire, and even when choosing a preferred candidate during a presidential debate. In this experiment, five identical pairs of white socks were displayed by attaching them vertically to a blue background, which was then mounted on an easel for viewing. One hundred participants from the University of Chester were used as subjects and asked to choose their preferred pair of socks. (a) Suppose each subject selects his or her preferred pair of socks at random. What is the probability that he or she would choose the pair of socks in the center position? (Enter your answer as a proportion rounded to one decimal place.) (b) What is the mean, μ , of the number of subjects who would choose the pair of socks in the center position? (Enter your answer as a whole number.) (c) What is the standard deviation, ?σ ? (Enter your answer as a whole number.) In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. In this experiment, 3434 subjects chose the pair of socks in the center. What is the probability, ?P , that 3434 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random? Use the Normal approximation first. If your software allows, find the exact binomial probability, ??Pe , and compare the two. (Enter your answers rounded to four decimal places.) P= Pe=

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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When choosing an item from a group, researchers have shown that an important factor influencing choice is the item's location. This occurs in varied situations such as shelf positions when shopping, filling out a questionnaire, and even when choosing a preferred candidate during a presidential debate. In this experiment, five identical pairs of white socks were displayed by attaching them vertically to a blue background, which was then mounted on an easel for viewing. One hundred participants from the University of Chester were used as subjects and asked to choose their preferred pair of socks.

(a) Suppose each subject selects his or her preferred pair of socks at random. What is the probability that he or she would choose the pair of socks in the center position? (Enter your answer as a proportion rounded to one decimal place.)

(b) What is the mean, μ , of the number of subjects who would choose the pair of socks in the center position? (Enter your answer as a whole number.)

In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. In this experiment, 3434 subjects chose the pair of socks in the center. What is the probability, ?P , that 3434 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random? Use the Normal approximation first. If your software allows, find the exact binomial probability, ??Pe , and compare the two. (Enter your answers rounded to four decimal places.)

P_e=

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(c) In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. In this experiment, 34 subjects chose the pair of socks in the center. What is the probability, ?, that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random? Use the Normal approximation first. If your software allows, find the exact binomial probability, ??, and compare the two. Give your answers to four decimal places.

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