Problem #1: Coke and Pepsi are the two most popular colas on the market. Do consumers prefer either one of the two brands of cola over the other? We conduct a matched pairs experiment as follows: 15 volunteers participate in a blind taste test. Each volunteer tastes both Coke and Pepsi (in random order) and scores the taste of each cola on a scale from 0 to 100. Some information that may be helpful is shown in the table below: Scores for Coke mean = 76.2 sd = 27 Scores for Pepsi Difference (d = Coke - Pepsi) mean = 80.3 mean -4.1 sd = 23 sd = 7.7 (a) Which of the following statements are true? (i) The scores for Coke and Pepsi for each individual are dependent. (ii) In order to conduct the matched pairs -test, we must assume the scores for Coke and the scores for Pepsi both follow t-distributions. (iii) In order to conduct the matched pairs t-test, we must assume that the differences in scores (Coke- Pepsi) follow a normal distribution. (A) (ii) and (iii) only (B) (i) and (iii) only (C) (i) and (ii) only (D) all of them (E) (i) only (F) none of them (G) (iii) only (H) (ii) only Problem #1(a): Select ↑ Part (a) choices. (b) What are the hypotheses for the appropriate test of significance? (A) Ho Hd = 0 vs Haμd <0 (B) Hod = 0 vs Had 0 (C) Hoμd = 0 vs Ha:µd > 0 (D) Ho: xd = 0 vs Ha: xd <0 (E) Hoμc = μp vs Нa: μc up (H) Ho: Xd=0 vs Ha: xd > 0 Problem #1(b): Select ↑ Part (b) choices.
Problem #1: Coke and Pepsi are the two most popular colas on the market. Do consumers prefer either one of the two brands of cola over the other? We conduct a matched pairs experiment as follows: 15 volunteers participate in a blind taste test. Each volunteer tastes both Coke and Pepsi (in random order) and scores the taste of each cola on a scale from 0 to 100. Some information that may be helpful is shown in the table below: Scores for Coke mean = 76.2 sd = 27 Scores for Pepsi Difference (d = Coke - Pepsi) mean = 80.3 mean -4.1 sd = 23 sd = 7.7 (a) Which of the following statements are true? (i) The scores for Coke and Pepsi for each individual are dependent. (ii) In order to conduct the matched pairs -test, we must assume the scores for Coke and the scores for Pepsi both follow t-distributions. (iii) In order to conduct the matched pairs t-test, we must assume that the differences in scores (Coke- Pepsi) follow a normal distribution. (A) (ii) and (iii) only (B) (i) and (iii) only (C) (i) and (ii) only (D) all of them (E) (i) only (F) none of them (G) (iii) only (H) (ii) only Problem #1(a): Select ↑ Part (a) choices. (b) What are the hypotheses for the appropriate test of significance? (A) Ho Hd = 0 vs Haμd <0 (B) Hod = 0 vs Had 0 (C) Hoμd = 0 vs Ha:µd > 0 (D) Ho: xd = 0 vs Ha: xd <0 (E) Hoμc = μp vs Нa: μc up (H) Ho: Xd=0 vs Ha: xd > 0 Problem #1(b): Select ↑ Part (b) choices.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Transcribed Image Text:Problem #1: Coke and Pepsi are the two most popular colas on the market. Do consumers prefer either one of the two brands
of cola over the other? We conduct a matched pairs experiment as follows: 15 volunteers participate in a blind
taste test. Each volunteer tastes both Coke and Pepsi (in random order) and scores the taste of each cola on a
scale from 0 to 100. Some information that may be helpful is shown in the table below:
Scores for Coke Scores for Pepsi Difference (d = Coke - Pepsi)
mean = 76.2
sd = 27
mean = 80.3
sd
=23
sd
mean -4.1
= 7.7
(a) Which of the following statements are true?
(i) The scores for Coke and Pepsi for each individual are dependent.
(ii) In order to conduct the matched pairs -test, we must assume the scores for Coke and the scores for
Pepsi both follow t-distributions.
(iii) In order to conduct the matched pairs t-test, we must assume that the differences in scores (Coke-
Pepsi) follow a normal distribution.
(A) (ii) and (iii) only (B) (i) and (iii) only (C) (i) and (ii) only (D) all of them (E) (i) only (F) none of them
(G) (iii) only (H) (ii) only
Problem #1(a): Select
↑ Part (a) choices.
(b) What are the hypotheses for the appropriate test of significance?
(A) Ho Hd 0 vs Ha: "d<0
(D) Hoxd 0 vs Ha: xd <0
(G) Ho: μC = up vs Ha:UC >
Problem #1(b): Select
↑ Part (b) choices.
(B) Ho: xd = 0 vs Ha: xd 0 (C) Hoμd = 0 vs Haμd > 0
(E) Ho μC =μP vs Ha: μC<μP (F) Ho: μd = 0 vs Haμd 0
up (H) Ho:Xd = 0 vs Ha:Xd >0
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Transcribed Image Text:Problem #1: Coke and Pepsi are the two most popular colas on the market. Do consumers prefer either one of the two brands
of cola over the other? We conduct a matched pairs experiment as follows: 15 volunteers participate in a blind
taste test. Each volunteer tastes both Coke and Pepsi (in random order) and scores the taste of each cola on a
scale from 0 to 100. Some information that may be helpful is shown in the table below:
Scores for Coke
mean -76.2
sd=27
Scores for Pepsi
mean
80.3
sd-23
Difference (d=Coke - Pepsi)
mean --4.1
sd = 7.7
(c) Assuming the appropriate assumptions are satisfied, what is the value of the test statistic for the appropriate
test of significance?
Problem #1(c):
answer correct to 2 decimals
(d) which is the correct interpretation of the p-value for the test in (b) and (c)?
(A) If the mean difference in the scores of Coke and Pepsi is 0, the probability of observing an average difference of
scores (defined as Coke-Pepsi) of -4.1 or more extreme (in either direction) is 0.0291.
(B) If the mean difference in the scores of Coke and Pepsi is not 0, the probability of observing an average
difference of scores (defined as Coke-Pepsi) of -4.1 or more extreme (in either direction) is 0.0583.
(C) If the scores of Coke are higher than the scores of Pepsi on average, then the probability of observing a mean
difference of -4.1 or less is 0.0583.
(D) If the scores of Coke are higher than the scores of Pepsi on average, then the probability of observing a mean
difference of -4.1 or less is 0.0291.
(E) If the scores of Pepsi are higher than the scores of Coke, on average, then the probability of observing a mean
difference of 4.1 or more is 0.0583.
(F) If the mean difference in the scores of Coke and Pepsi is not 0, the probability of observing an average
difference of scores (defined as Coke-Pepsi) of -4.1 or more extreme (in either direction) is 0.0291.
(G) If the mean difference in the scores of Coke and Pepsi is 0, the probability of observing an average difference of
scores (defined as Coke-Pepsi) of -4.1 or more extreme (in either direction) is 0.0583.
(H) If the scores of Pepsi are higher than the scores of Coke, on average, then the probability of observing a mean
difference of 4.1 or more is 0.0291.
Problem #1: Select Part (8) choices.
Solution
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