1. You have run an experiment to test whether there is a hypothetical bias in people's willingness to pay for chocolate bars containing Fair Trade certified cocoa when buying their groceries. In a within-subject design, you ask 8 randomly selected shoppers at New World their hypothetical willingness to pay (WTP) for a large Fair Trade certified chocolate bar. You then elicit their actual WTP for the same bars using a demand-revealing auction mechanism. This experiment yields the following information: TI: hypothetical WTP ($) TII: actual WTP ($) Subject 3 4 5 6 7 8 4.70 4.70 3.00 3.75 1.10 3.65 4.60 2.40 3.30 .45 1 2 3.20 3.20 2.15 3.00 3.30 1.10 a. Manually use the sign test to test whether the populations from which the two treatment results are drawn are significantly different. Please indicate the significance level at which a null hypothesis of "no difference" can be rejected for a two tailed test. Could you reject the null at a conventional significance level like 5%? Please show all your work and make your reasoning explicit at every step. b. Now manually use the Wilcoxon signed rank test to test whether the populations from which the two treatment results are drawn are the same (i.e. have the same medians and distributions). Please indicate the significance level at which a null hypothesis of "no difference" can be rejected for a two tailed test. Could you reject the null at a conventional significance level like 5%? Please show all your work and make your reasoning explicit at every step. c. Why in this particular example might the sign test and signed rank test give you different answers as to whether the populations from which your samples are drawn are significantly different? Explain.
1. You have run an experiment to test whether there is a hypothetical bias in people's willingness to pay for chocolate bars containing Fair Trade certified cocoa when buying their groceries. In a within-subject design, you ask 8 randomly selected shoppers at New World their hypothetical willingness to pay (WTP) for a large Fair Trade certified chocolate bar. You then elicit their actual WTP for the same bars using a demand-revealing auction mechanism. This experiment yields the following information: TI: hypothetical WTP ($) TII: actual WTP ($) Subject 3 4 5 6 7 8 4.70 4.70 3.00 3.75 1.10 3.65 4.60 2.40 3.30 .45 1 2 3.20 3.20 2.15 3.00 3.30 1.10 a. Manually use the sign test to test whether the populations from which the two treatment results are drawn are significantly different. Please indicate the significance level at which a null hypothesis of "no difference" can be rejected for a two tailed test. Could you reject the null at a conventional significance level like 5%? Please show all your work and make your reasoning explicit at every step. b. Now manually use the Wilcoxon signed rank test to test whether the populations from which the two treatment results are drawn are the same (i.e. have the same medians and distributions). Please indicate the significance level at which a null hypothesis of "no difference" can be rejected for a two tailed test. Could you reject the null at a conventional significance level like 5%? Please show all your work and make your reasoning explicit at every step. c. Why in this particular example might the sign test and signed rank test give you different answers as to whether the populations from which your samples are drawn are significantly different? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

Transcribed Image Text:1. You have run an experiment to test whether there is a hypothetical bias in
people's willingness to pay for chocolate bars containing Fair Trade certified cocoa
when buying their groceries. In a within-subject design, you ask 8 randomly
selected shoppers at New World their hypothetical willingness to pay (WTP) for a
large Fair Trade certified chocolate bar. You then elicit their actual WTP for the same
bars using a demand-revealing auction mechanism.
This experiment yields the following information:
TI: hypothetical WTP ($)
TII: actual WTP ($)
Subject
3 4 5 6 7 8
4.70 4.70 3.00 3.75 1.10
3.65 4.60 2.40 3.30 .45
1 2
3.20 3.20 2.15
3.00 3.30 1.10
a. Manually use the sign test to test whether the populations from which the two
treatment results are drawn are significantly different. Please indicate the significance
level at which a null hypothesis of "no difference" can be rejected for a two tailed test.
Could you reject the null at a conventional significance level like 5%?
Please show all your work and make your reasoning explicit at every step.
b. Now manually use the Wilcoxon signed rank test to test whether the populations
from which the two treatment results are drawn are the same (i.e. have the same
medians and distributions). Please indicate the significance level at which a null
hypothesis of "no difference" can be rejected for a two tailed test. Could you reject
the null at a conventional significance level like 5%?
Please show all your work and make your reasoning explicit at every step.
c. Why in this particular example might the sign test and signed rank test give you
different answers as to whether the populations from which your samples are drawn
are significantly different? Explain.
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