Question 2 Data Number of Times "Feed Both" Option Was Chosen No Chimp in Chimp in Chimp Adjoining Cage Adjoining Cage 21 23 N 22 22 23 21 21 23 autw 18 19 16 19 19 19 3. A survey was conducted to investigate how people use the nutritional information provided on food package labels. Interviews were conducted with 1003 randomly selected adults, and each participant was asked a series of questions, including the following one: When purchasing packaged food, how often do you check the nutrition labeling on the package? It was reported that 582 responded "frequently" to this question about checking labels. a) Construct a 90% confidence interval for the proportion of people who frequently check the nutrition labeling on a package. b) Based on these data, is it reasonable to conclude that a majority of adults frequently check the nutritional labels when purchasing packaged foods? Use a 0.05 level of significance. i. Use the critical value approach. i. Use the p-value approach. 4. The question on whether people who work long hours have more trouble sleeping was examined in a study on sleep patterns. Two random samples of university employees were selected, all of whom were employed full-time and worked at least 35 hours per week. The researchers found that 750 of the 1 501 employees who work more than 40 hours per week usually get less than 7 hours of sleep a night, while 407 of the 958 employees who work between 35 and 40 hours per week usually get less than 7 hours of sleep a night. Let: P1 = Proportion of university employees who work at least 40 hours per week p2 = Proportion of university employees who work 35 - 40 hours per week p = Pooled proportion of usually employees who get less than 7 hours of sleep a night a) Calculate the following point estimates i. p1, the point estimate for P1 ii. pz, the point estimate for pz ili. p, the point estimate for p iv. (p1 - p2), the point estimate for the difference in proportions.BME 120 ASSIGNMENT 2 GROUP B 1. A study was conducted to investigate the relationship between depression and chocolate consumption. Participants in the study were 931 adults who were not currently taking medication for depression. These participants were screened for depression using a widely used screening test. The participants were then divided into two samples based on the score on the screening test. One sample consisted of people who screened positive for depression, and the other sample consisted of people who did not screen positive for depression. Each of the study participants also completed a food frequency survey, including questions on chocolate consumption. The researchers believed that the two samples were representative of the two populations of interest- adults who would screen positive for depression and adults who would not screen positive. The data are summarised below: Group Sample Mean Standard Size Deviation Participants who screened positive 311 8.39 14.83 Participants who screened negative 620 5.39 3.76 a) Use a hypothesis test to determine, at a 0.10 level of significance, whether these data provide evidence that, on average, participants who screened positive for depression are more likely to consume chocolate. Use the critical value approach. ii. Use the p-value approach. b) Construct a 95% confidence interval for the difference between the chocolate consumption of participants who screened positive and those who screened negative for depression, and interpret this interval. 2. Researchers were interested to know if chimpanzees are charitable, i.e. will take advantage of opportunities to deliver benefits to individuals at no cost to themselves. An experiment was designed in which a sample of chimpanzees was trained to use an apparatus that would deliver food just to the subject chimpanzee when one lever was pushed and would deliver food to both the subject chimpanzee and another chimpanzee in an adjoining cage when another lever was pushed. After training, the chimps were observed when there was no chimp in the adjoining cage and when there was another chimp in the adjoining cage. The researchers hypothesized that if chimpanzees were motivated by the welfare of others, they would choose the option that provided food to both chimpanzees more often when there was a chimpanzee in the adjoining cage. Data on the number of times the "feed both" option was chosen out of 36 opportunities are given in the accompanying table on the next page. Test at a 0.01 level of significance if chimpanzees are indeed charitable