The paper “Mood Food: Chocolate and Depressive Symptoms in a Cross-Sectional Analysis” (Archives of Internal Medicine [2010]: 699–703) describes a study that investigated 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.
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 paper reported that the mean number of servings of chocolate for the sample of people that screened positive for depression was 8.39 servings per month and the sample standard deviation was 14.83. For the sample of people who did not screen positive for depression, the mean number of servings per month was 5.39 and the standard deviation was 8.76. The paper did not say how many individuals were in each sample, hut for the purposes of this exercise, you can assume that the 931 study participants were divided into 311 who screened positive for depression and 620 who did not screen positive.
Estimate the difference in the mean number of servings of chocolate per month in the population of people who would screen positive for depression and the mean number of chocolate servings per month in the population of people who would not screen positive for depression. Use a confidence level of 90% and be sure to interpret the interval in context.
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Chapter 11 Solutions
Introduction to Statistics and Data Analysis
- According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in the U.S. in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumers ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a different proportion of identity theft than 23%? Test at 5% level.arrow_forwardA particular paper described a study of children who were underweight or normal weight at age 2. Children in the sample were classified according to the number of sweet drinks consumed per day and whether or not the child was overweight one year after the study began. Is there evidence of an association between whether or not children are overweight after one year and the number of sweet drinks consumed? Assume that it is reasonable to regard the sample of children in this study as representative of 2 to 3 years old children and then test the appropriate hypotheses using a .05 significance level. (Round your answer to two decimal places.) Number of Sweet Overweight? Drinks Consumed per Day Yes No 22 930 1 73 2071 2 56 1681 3 or More 102 3389 x2 = | P-value interval Op< 0.001 O 0.001 s p < 0.01 O 0.01 sp < 0.05 O 0.05 sp < 0.10 Op2 0.10 There is --Select--- v to conclude that there is an association between whether or not children are overweight after one year and the number of sweet…arrow_forwardCallahan (2009) conducted a study to evaluate the effectiveness of physical exercise programs for individuals with chronic arthritis. Participants with doctor-diagnosed arthritis either received a Tai Chi course immediately or were placed in a control group to begin the course 8 weeks later. At the end of the 8-week period, self-reports of pain were obtained for both groups. Data similar to the results obtained in the study are shown in the following table. Self-Reported Level of Pain Mean Mean SE Tai Chi course 3.7 1.2 No Tai Chi course 7.6 1.7 Construct a bar graph that…arrow_forward
- One study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators then asked about the use of cell phones. Result: “Our data suggest that the use of hand- held cellular phones is not associated with risk of brain cancer. B . Based on this study, can you determine that cellular use does not CAUSE brain cancer? Why or why not?arrow_forwardThe National Highway traffic Safety Administration requires each U.S. state to carry out an observational study to assess the level of seat belt use in the state. One report summarized data from a study done in a certain state. The proportions in the accompanying table are based on observations of over 25,000 drivers and passengers. Uses Seatbelt Does Not Use Seat Belt Male 0.425 0.075 Female 0.452 0.048 Assume that these proportions are representative of adults in this state and that an adult from this state is selected at random. (a) What is the probability that the selected adult uses a seat belt? (b) What is the probability that the selected adult uses a seat belt given that the individual selected is male?arrow_forwardThe article "Vehicle-Arrival Characteristics at Urban Uncontrolled Intersections" (V. Rengaraju and V. Rao, Journal of Transportation Engineering, 1995: 317-323) presents data on traffic characteristics at 10 intersections in Madras, India. One characteristic measured was the speeds of the vehicles traveling through the intersections. The accompanying table gives the 15th, 50th, and 85th percentiles of speed (in km/h) for two intersections. Percentile Intersection 15th 50th 85th 27.5 37.5 40.0 в 24.5 26.5 36.0 If a histogram for speeds of vehicles through intersection A were drawn, would it most likely be skewed to the left, skewed to the right, or approximately symmetric? Explain. b. If a histogram for speeds of vehicles through intersection B were drawn, would it most likely be skewed to the left, skewed to the right, or approximately symmetric? Explain. a.arrow_forward
- Thanh Nguy.. Empathy: The Interpersonal Reactivity Index is a survey designed to assess four different types of empathy. One type of empathy, called Empathetic Concern, measures the tendency to feel sympathy and compassion for people who are less fortunate. The index ranges from 0 (less empathetic) to 28 (more empathetic). The following data, representing random samples of 12 males and 12 females, are consistent with results reported in psychological studies. Boxplots show that it is reasonable to assume that the populations are approximately normal. Can you conclude that the mean empathy score for men is less than the mean empathy score for women? Let u, denote the mean empathy score for men. Use the a = 0.01 level and the P-value method with the TI-84 Plus calculator. Males 20 12 16 13 26 21 23 15 18 25 15 Females 22 20 26 25 28 24 16 19 20 23 21 23 Send data to Excel Part 1 of 4 State the null and alternate hypotheses. i = ':°H i 'i:'H test. The hypothesis test is a two-tailed Part:…arrow_forwardA sample survey by Comcast asked a random sample of customers about use of the Internet and about the type of community they lived in. Here are the results: Internet Users: Rural: 433 Suburban: 1072 Urban: 536 Nonusers: Rural: 463 Suburban: 627 Urban: 388 Is there a relationship between Internet use and community type? Give statistical evidence to support your findings.arrow_forwardResearchers asked soda drinkers to view either the logo for their favorite soda or a graphic warning demonstrating the harmful effects of sugary beverages (e.g., tooth decay, obesity) and then measured their negative mood with a short survey. They found that those participants who saw the warnings reported significantly greater negative moods than those who saw the logos. Which statistical test should be used?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt