Homework Help is Here – Start Your Trial Now!
Math
Statistics
A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket. Each shopper was asked whether they had bought any wine in each of the last 4 weeks. Let x denote the number of weeks when a shopper bought wine and f denote the number of shoppers who bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first two rows of the following table. Note that f = 34 shoppers did not buy any wine, f = 40 shoppers bought wine only in 1 of those 4 weeks and so on. 2 3 Total 34 40 64 56 6 200 Pi 0.0915 0.2995 0.3675 0.2005 0.0410 It has been suggested that these data are binomially distributed with n = 4 and some (unknown) parameter p, which is the probability that a randomly selected shopper will buy wine in any given week. Answer the following questions. a. Calculate the sample mean and the sample variance for these data. b. Estimate the parameter p for the suggested binomial distribution. c. Write down the formula to calculate the binomial probability P( X = 3) = 0.2005 (4dp), as given in the table. Show clearly how to use the answer from part (b) to calculate the probability given here. d. Use the p;-values given in the table, which were obtained as in part (c), to calculate corresponding expected values, e;. Give your expected values to 1 decimal place. e. Do a goodness-of-fit test on these data, using a 5% level of significance. f. Comment briefly on the result of the test.

A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket. Each shopper was asked whether they had bought any wine in each of the last 4 weeks. Let x denote the number of weeks when a shopper bought wine and f denote the number of shoppers who bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first two rows of the following table. Note that f = 34 shoppers did not buy any wine, f = 40 shoppers bought wine only in 1 of those 4 weeks and so on. 2 3 Total 34 40 64 56 6 200 Pi 0.0915 0.2995 0.3675 0.2005 0.0410 It has been suggested that these data are binomially distributed with n = 4 and some (unknown) parameter p, which is the probability that a randomly selected shopper will buy wine in any given week. Answer the following questions. a. Calculate the sample mean and the sample variance for these data. b. Estimate the parameter p for the suggested binomial distribution. c. Write down the formula to calculate the binomial probability P( X = 3) = 0.2005 (4dp), as given in the table. Show clearly how to use the answer from part (b) to calculate the probability given here. d. Use the p;-values given in the table, which were obtained as in part (c), to calculate corresponding expected values, e;. Give your expected values to 1 decimal place. e. Do a goodness-of-fit test on these data, using a 5% level of significance. f. Comment briefly on the result of the test.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Topic Video
Question
A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket. Each shopper was asked whether they had bought any wine in each of the last 4 weeks. Let x denote the number of weeks when a shopper bought wine and f denote the number of shoppers who bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first two rows of the following table. Note thatf = 34 shoppers did not buy any wine, f = 40 shoppers bought wine only in 1 of those 4 weeks and so on. 1 2 3 Total fi 34 40 64 56 200 Pi 0.0915 0.2995 0.3675 0.2005 0.0410 It has been suggested that these data are binomially distributed with n= 4 and some (unknown) parameter p, which is the probability that a randomly selected shopper will buy wine in any given week. Answer the following questions. a. Calculate the sample mean and the sample variance for these data. b. Estimate the parameter p for the suggested binomial distribution. c. Write down the formula to calculate the binomial probability P( X = 3) = 0.2005 (4dp), as given in the table. Show clearly how to use the answer from part (b) to calculate the probability given here. d. Use the p;-values given in the table, which were obtained as in part (c), to calculate corresponding expected values, e;. Give your expected values to 1 decimal place. e. Do a goodness-of-fit test on these data, using a 5% level of significance. f. Comment briefly on the result of the test.
Transcribed Image Text:A survey of 200 shoppers was conducted to investigate how often people buy wine at a certain supermarket. Each shopper was asked whether they had bought any wine in each of the last 4 weeks. Let x denote the number of weeks when a shopper bought wine and f denote the number of shoppers who bought wine in x weeks. If a shopper had not bought any wine then x was set to zero. Results are given in the first two rows of the following table. Note thatf = 34 shoppers did not buy any wine, f = 40 shoppers bought wine only in 1 of those 4 weeks and so on. 1 2 3 Total fi 34 40 64 56 200 Pi 0.0915 0.2995 0.3675 0.2005 0.0410 It has been suggested that these data are binomially distributed with n= 4 and some (unknown) parameter p, which is the probability that a randomly selected shopper will buy wine in any given week. Answer the following questions. a. Calculate the sample mean and the sample variance for these data. b. Estimate the parameter p for the suggested binomial distribution. c. Write down the formula to calculate the binomial probability P( X = 3) = 0.2005 (4dp), as given in the table. Show clearly how to use the answer from part (b) to calculate the probability given here. d. Use the p;-values given in the table, which were obtained as in part (c), to calculate corresponding expected values, e;. Give your expected values to 1 decimal place. e. Do a goodness-of-fit test on these data, using a 5% level of significance. f. Comment briefly on the result of the test.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS