ExtraCredit-04: Problem 3 Problem Value: 1 point(s). Problem Score: 42%. Attempts Remaining: Unlimited. (1 point) Office occupancy in a city is an indication of the economic health of the region in which it is located. Suppose a random sample of offices in Boston and Chicago was selected and the number of vacancies was recorded. Round all answers to four decimal places. City Vacant Not Vacant Total Boston 21 117 138 Chicago 12 100 112 Total 33 217 250 Our research question is, "Is there a difference in the vacancy rates for these two cities?" 1. What are the hypotheses for testing whether there is a difference? Ho: The variables City and Vacancy are independent . The difference in the vacancy rates in the sample data is due to chance. HA: The variables are not independent v . The difference in the vacancy rates is not v due to chance. 2. Calculate the difference in vacancy rates for these two cities: P Boston - P Chicago = 3. The paragraph below describes the setup for a randomization test. We write Boston on cards and Chicago on cards. Then we shuffle the cards and split them into two groups: one group of size representing vacant offices and one group of size representing occupied offices. We calculate the proportion of Boston offices that are vacant and subtract the proportion of Chicago offices that are vacant to get p Boston,sim - P Chicago, sim and build a histogram of this simulated differences. Use the Two Proportion Resampling Test app embedded below to do this. Use this external link to the Two Proportion Resampling Test if the app does not load properly on your computer. (Right click to open in a new tab or window.)4. Choosing the "beyond" option for the counted samples and shuffling at least 3000 times, what is the approximate p-value for the hypothesis test? p-value = 5. Cheryl takes a different sample and conducts the hypothesis test. She gets a p-value of 0.0014. How much evidence does Cheryl have that the null model is not a good fit for her observed result? O A. Little O B. Some O C. Strong O D. Very Strong O E. Extremely Strong that the null model is not a good fit for our observed data.ExtraCredit-04: Problem 4 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: Unlimited. (1 point) Gardasil Completion ~ HPV (human papillomavirus) is a virus that has been linked to the development of cervical and other cancers. The Gardasil vaccine for HPV has been available since 2006 and was initially recommended by the FDA for use by women aged 9 - 26. At the time, the typical Gardasil regimen consisted of a sequence of three shots given over a 6- to 12-month period. (Current recommendations are for routine vaccination for all children starting at age 11 and for anyone through age 26 who has not been adequately vaccinated. Because patients need to return to a clinic to receive the follow-up shots, medical professionals are concerned about completion rates for vaccine series. In an effort to learn what variables might contribute to a patient completing the series, an early study in 2008 examined the medical records of 1,413 young female patients aged 11-26 years in the Baltimore area who came to one of four clinics to begin the three-shot regimen. Information on the number of shots the patient received and the clinic location was recorded. Let's consider the 1,413 patients from the Gardasil investigation as a random sample of female patients from that time period and use a randomization-based hypothesis test to answer the research question, "Are the variables Clinic Location and Completion Status independent?" not Clinic location Completed Did complete Total series series Suburban 355 608 963 Urban 114 336 450 Tota 469 944 1413 a. Calculate the observed difference in the proportion of patients from suburban clinics and urban clinics who completed the series of vaccinations. P Suburban - PUrban = b. Select from the dropdowns to complete the null and alternative hypotheses that are appropriate to test this research question. Ho: The variables Clinic Location and Completion Status ? independent. The observed difference ? due to chance. Ha: The variables Clinic Location and Completion Status ? independent. The observed difference ? due to chance. c. To set up a randomization procedure using colored cards, how many cards would we need? i. How many of these cards should be green to represent patients at suburban clinics? ii. How many of these cards should be white to represent patients at urban clinics? After we shuffle the cards: a. How many should be placed in a pile representing those who completed the series? b. How many should be place in a pile representing those who did not complete the series? We then calculate the difference between the proportion of cards representing patients from suburban clinics and urban clinics who completed the series of vaccinations and call it P Suburban, sim - PUrban, sim a. If we repeat the randomization procedure many times, and construct a dotplot of the simulated differences P Suburban,sim - PUrban,sim, where would you expect the distribution to be centered? b. When we look at the dotplot of simulated differences, there are no results beyond the observed difference, P Suburban - PUrbanExtraCredit-04: Problem 6 Problem Value: 1 point(s). Problem Score: 94%. Attempts Remaining: Unlimited. (1 point) A 20-minute consumer survey mailed to 300 adults aged 25-34 included a $5 Starbucks gift certificate. The same survey was mailed to 300 adults aged 25-34 without the gift certificate. There were 45 responses from the first group and 23 from the second group. Use the table below to summarize this information. Round all answers to four decimal places Group Responded Did not respond Total Gift Card 45 255 300 No Gift Card 23 277 300 Total 68 532 600 The company wants to know if the response rates for people who receive a gift certificate is higher than for people who do not. We will conduct a hypothesis test. 1. What are the hypotheses for this testing scenario? Ho: The variables Responded and Card v are independent . The difference in the response rates in the sample data is v due to chance. HA: The variables are not independent v . The response rate in the gift card group is greater than v the response rate in the no gift card group. 2. Calculate the difference in response rates for these two groups: P Card- P NoCard = .07333 3. The paragraph below describes the setup for a randomization test. We write gift card on 300 cards and no gift card on 300 cards. Then we shuffle the cards and split them into two groups: one group of size 68 representing people who responded to the survey and one group of size 532 representing people who did not respond to the survey. We calculate the proportion of the gift card group that responded and subtract the proportion of the no gift card group to get p Card,sim- P NoCard,sim and build a histogram of this simulated differences. Use the Two Proportion Resampling Test app embedded below to do this. Use this external link to the Two Proportion Resampling Test if the app does not load properly on your computer. (Right click to open in a new tab or window.)4. Choosing the "greater than" option for the counted samples and shuffling at least 3000 times, what is the approximate p-value for the hypothesis test, rounded to three decimal places? p-value = 5. The company repeated this experiment with a different sample and conducted a hypothesis test using the same hypotheses. This time they obtained a p-value of 0.0415. For this second hypothesis test, how much evidence do they have that the null model is not a good fit for their data? O A. extremely strong evidence O B. strong evidence O C. very strong evidence O D. some evidence O E. little evidence