MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The Condé Nast Traveler Gold List for 2012 provided ratings for the top 20 small cruise ships.† The data shown below are the scores each ship received based upon the results from Condé Nast Traveler's Annual Readers' Choice Survey. Each score represents the percentage of respondents who rated a ship as excellent or very good on several criteria, including Itineraries/Schedule, Shore Excursions, and Food/Dining. An overall score was also reported and used to rank the ships. The highest ranked ship, the Seabourn Odyssey, has an overall score of 94.4, the highest component of which is 97.8 for Food/Dining.
Ship | Overall | Itineraries/ Schedule |
Shore Excursions |
Food/ Dining |
---|---|---|---|---|
Seabourn Odyssey | 94.4 | 94.6 | 90.9 | 97.8 |
Seabourn Pride | 93.0 | 96.7 | 84.2 | 96.7 |
National Geographic Endeavor | 92.9 | 100.0 | 100.0 | 88.5 |
Seabourn Sojourn | 91.3 | 88.6 | 94.8 | 97.1 |
Paul Gauguin | 90.5 | 95.1 | 87.9 | 91.2 |
Seabourn Legend | 90.3 | 92.5 | 82.1 | 98.8 |
Seabourn Spirit | 90.2 | 96.0 | 86.3 | 92.0 |
Silver Explorer | 89.9 | 92.6 | 92.6 | 88.9 |
Silver Spirit | 89.4 | 94.7 | 85.9 | 90.8 |
Seven Seas Navigator | 89.2 | 90.6 | 83.3 | 90.5 |
Silver Whisperer | 89.2 | 90.9 | 82.0 | 88.6 |
National Geographic Explorer | 89.1 | 93.1 | 93.1 | 89.7 |
Silver Cloud | 88.7 | 92.6 | 78.3 | 91.3 |
Celebrity Xpedition | 87.2 | 93.1 | 91.7 | 73.6 |
Silver Shadow | 87.2 | 91.0 | 75.0 | 89.7 |
Silver Wind | 86.6 | 94.4 | 78.1 | 91.6 |
SeaDream II | 86.2 | 95.5 | 77.4 | 90.9 |
Wind Star | 86.1 | 94.9 | 76.5 | 91.5 |
Wind Surf | 86.1 | 92.1 | 72.3 | 89.3 |
Wind Spirit | 85.2 | 93.5 | 77.4 | 91.9 |
(a)
Determine the estimated regression equation that can be used to predict the overall score given the scores for Itineraries/Schedule, Shore Excursions, and Food/Dining. (Let x1 represent Itineraries/Schedule, x2 represent Shore Excursion, x3 represent Food/Dining, and y represent Overall score. Round your constant term to one decimal place and coefficients to two decimal places.)
ŷ = ??
(b)
Use the F test to determine the overall significance of the relationship.
State the null and alternative hypotheses.
-H0: One or more of the parameters is not equal to zero.
Ha: ?1 = ?2 = ?3 = 0
Ha: ?1 = ?2 = ?3 = 0
-H0: ?1 = ?2 = ?3 = 0
Ha: All the parameters are not equal to zero.
Ha: All the parameters are not equal to zero.
- H0: ?1 = ?2 = ?3 = 0
Ha: One or more of the parameters is not equal to zero.
Ha: One or more of the parameters is not equal to zero.
-H0: ?0 ≠ 0
Ha: ?0 = 0
Ha: ?0 = 0
-H0: ?0 = 0
Ha: ?0 ≠ 0
Ha: ?0 ≠ 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value =??
What is your conclusion at the 0.05 level of significance?
-Do not reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.
-Do not reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.
-Reject H0. There is insufficient evidence to conclude that there is a significant relationship among the variables.
-Reject H0. There is sufficient evidence to conclude that there is a significant relationship among the variables.
(c)
Use the t test to determine the significance of each independent variable.
State the null and alternative hypotheses for Itineraries/Schedule.
-H0: ?1 ≠ 0
Ha: ?1 = 0
Ha: ?1 = 0
-H0: ?1 = 0
Ha: ?1 ≠ 0
Ha: ?1 ≠ 0
- H0: ?1 ≤ 0
Ha: ?1 > 0
Ha: ?1 > 0
-H0: ?1 = 0
Ha: ?1 > 0
Ha: ?1 > 0
-H0: ?1 ≥ 0
Ha: ?1 < 0
Ha: ?1 < 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
What is your conclusion at the 0.05 level of significance?
-Do not reject H0. There is insufficient evidence to conclude that Itineraries/Schedule is a significant factor.
-Reject H0. There is insufficient evidence to conclude that Itineraries/Schedule is a significant factor.
-Do not reject H0. There is sufficient evidence to conclude that Itineraries/Schedule is a significant factor.
-Reject H0. There is sufficient evidence to conclude that Itineraries/Schedule is a significant factor.
State the null and alternative hypotheses for Shore Excursions.
-H0: ?2 ≠ 0
Ha: ?2 = 0
Ha: ?2 = 0
-H0: ?2 ≥ 0
Ha: ?2 < 0
Ha: ?2 < 0
- H0: ?2 = 0
Ha: ?2 ≠ 0
Ha: ?2 ≠ 0
-H0: ?2 ≤ 0
Ha: ?2 > 0
Ha: ?2 > 0
-H0: ?2 = 0
Ha: ?2 > 0
Ha: ?2 > 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
What is your conclusion at the 0.05 level of significance?
-Do not reject H0. There is sufficient evidence to conclude that Shore Excursions is a significant factor.
-Reject H0. There is insufficient evidence to conclude that Shore Excursions is a significant factor.
-Do not reject H0. There is insufficient evidence to conclude that Shore Excursions is a significant factor.
-Reject H0. There is sufficient evidence to conclude that Shore Excursions is a significant factor.
State the null and alternative hypotheses for Food/Dining.
-H0: ?3 ≥ 0
Ha: ?3 < 0
Ha: ?3 < 0
-H0: ?3 ≤ 0
Ha: ?3 > 0
Ha: ?3 > 0
-H0: ?3 = 0
Ha: ?3 > 0
Ha: ?3 > 0
-H0: ?3 = 0
Ha: ?3 ≠ 0
Ha: ?3 ≠ 0
-H0: ?3 ≠ 0
Ha: ?3 = 0
Ha: ?3 = 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Test statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
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