GW 2.15

docx

School

Florida International University *

*We aren’t endorsed by this school

Course

2122

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by MasterDiscovery11757

Lab Module 3: Estimating Conditional Probabilities and Assessing Statistical Independence Question 1: In your role as Events Director for Carnival Cruises, you routinely ask disembarking cruise passengers returning from a 7-day cruise to the Bahamas: ”What was your favorite activity during your stay with Carnival Cruises?” and also collect demo- graphic information from the respondents. The data table below reflects the frequency of responses about Favorite Cruise Activity cross-tabulated by Age Group in a sample of N = 5,049 young and young adult passengers. Favorite Cruise Activity Among N = 5,325 Young and Young Adult Passengers Shore Excursions Pool Deck Shows/Nightlife Fine Dining Total Ages 12 - 18 674 118 96 19 907 Ages 19 - 26 721 338 161 208 1,428 Ages 27 - 35 652 780 610 672 2,714 Total 2,047 1,236 867 899 5,049 a) Estimate the probability that a young/young adult passenger states that the Pool Deck is their favorite activity. 1236/5049= 0.245 b) Estimate the probability that a young/young adult passenger states that Shore Ex- cursions is their favorite activity. 2047/5049= 0.405 c) Which activity is more popular among young/young adult passengers: the Pool Deck or Shore Excursions?

Shore excursions d) Estimate the conditional probability that a young passenger states that Shore Ex- cursions is their favorite activity given that the passenger is between the ages of 12- 18. 674/907= 0.74 e) Estimate the conditional probability that a young adult passenger states that Shore Excursions is their favorite activity given that the passenger is between the ages of 27- 35. 652/2714= 0.24 f) How much more likely is a young adult passenger aged 27-35 to state that Shore Excursions is his or her favorite activity compared to a young passenger between the ages of 12-18? Is 50% less likely for a young adult passenger aged 27-35. 0.24/0.74= 1/3= 3 times less likely. g) How much more likely is a young adult passenger aged 27-35 to state that Fine

Dining is his or her favorite activity compared to a young passenger between the ages of 12-18? 27-35) 672/2714= 0.25, 12-18) 19/907=0.021. Around 25% more likely h) Which cruise activity is the most likely to be reported as the favorite for each age group? Shore Excursions for ages between 12-26 and Pool deck for ages between 27-35. Question 2: The data table below reflects the frequency of responses about Favorite Cruise Activity cross-tabulated by Gender in a sample of N = 5,049 young and young adult passengers. Favorite Cruise Activity Among N = 5,325 Young and Young Adult Passengers Shore Excursions Pool Deck Shows/Nightlife Fine Dining Total Male 1,298 570 256 224 2,348 Female 749 666 611 675 2,701 Total 2,047 1,236 867 899 5,049 a) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is male. 1298/2348= 0.553 b) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is female.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

749/2701= 0.277 c) How much more likely is a male young/young adult passenger to state that Shore Excursions is his favorite activity compared to a female young/young adult passenger? 0.37/0.63= 2 times more likely d) Assume Favorite Cruise Activity and Gender are statistically independent. Fill in the expected cross-tabulation table below. Shore Excursions Pool Deck Shows/Nightlife Fine Dining Total Male 2,348 Female 2,701 Total 2,047 1,236 867 899 5,049 P(male and shore)= P(male) 2348/5049 x P(shore) 2047/5049* 5049= 952 P(male and pool)= 575 P(male and nightlife) = 403 P(male and fine dining)= 418 P female: shore= 1095, pool deck=661, nightlife= 464, dining= 481

e) Compare the expected and observed cross-tabulation tables. For which favorite cruise activities do the expected and observed cross-tabulation tables differ by the largest extent? f) Compute the statistic T = P i (Observed i − Expected i ) 2 Expected i for the cross-tabulated data above. Does the data indicate that Favorite Cruise Activity is statistically independent of gen- der? Lab Module 3 - Worksheet Question 3: The data tables below reflect the frequency of responses about Favorite Cruise Activity cross-tabulated by Age Group and separated by Gender into two tables (2,348 Males and 2,701 Females). Favorite Cruise Activity Among N = 2,348 Young and Young Adult Male Passengers Shore Excursions Pool Deck Shows/Nightlife Fine Dining Total Ages 12 - 18 354 57 43 7 461 Ages 19 - 26 471 105 80 44 700 Ages 27 - 35 473 408 133 173 1,187 Total 1,298 570 256 224 2,348 Favorite Cruise Activity Among N = 2,701 Young and Young Adult Female Passengers Shore Excursions Pool Deck Shows/Nightlife Fine Dining Total Ages 12 - 18 320 61 53 12 446 Ages 19 - 26 250 233 81 164 728 Ages 27 - 35 179 372 477 499 1,527 Total 749 666 611 675 2,701 The following graphic depicts the conditional probability that a young/young adult pas- senger states that Fine Dining is their favorite cruise activity given their age group and gender. Estimated P(Fine Dining is Favorite Cruise Activity | Age Group & Gender) The conditional probability that a young/young adult passenger states that Fine

Dining is their favorite cruise activity increases with increasing age group. The rate of increase is higher in females than males, who at ages between 27 - 35, are more than twice as Lab Module 3 - Worksheet likely than males to state that fine dining is their favorite cruise activity. a) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is male and between the ages of 12-18. b) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is male and between the ages of 19-26. c) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is male and between the ages of 27-35. d) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is female and be- tween the ages of 12-18. e) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is female and be- tween the ages of 19-26. f) Estimate the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite activity given that the passenger is female and be- tween the ages of 27-35. g) Graph the results you obtain in a-f above, depicting the conditional probability that a young/young adult passenger states that Shore Excursions is their favorite cruise activ- ity given their age group and gender. h) What insights can you derive from your graph, with respect to which age group and gender is most likely to state that Shore Excursions is their favorite cruise activity? How

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

might these results be useful in your role as Events Director for Carnival Cruises? i) What other insights can you glean from this data? 1.2 1.36

GW 2.15

Related Documents