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=

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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=

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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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