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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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.5: Interpreting Data
Problem 1C
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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.
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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