Risk and odds ratios 7/7: What do you conclude from the relative risk and odds ratio?

A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate? The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position. The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position. Because we would be interested in any…

Do Left-Handers Die Earlier? According to a study published in the Journal of the American Public Health Association, lefthanded people do not die at an earlier age than right-handed people, contrary to the conclusion of a highly publicized report done 2 years earlier. The investigation involved a 6-year study of 3800 people in East Boston older than age 65. Researchers at Harvard University and the National Institute of Aging found that the “lefties” and “righties” died at exactly the same rate. “There was no difference, period,” said Dr. J. Guralnik, an epidemiologist at the institute and one of the coauthors of the report.

The cost of attending your college has once again gone up. Although you have been told that education is investment in human capital, which carries a return of roughly 10% a year, you (and your parents) are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings.Next you perform the following regression  cost^= = 7,311.17 + 3,985.20 × Reputation – 0.20 × Size              (2,058.63)     (664.58)                        (0.13) + 8,406.79 × Dpriv – 416.38 × Dlibart – 2,376.51 × Dreligion(2,154.85)    (1,121.92)               (1,007.86) R2=0.72, SER=3,773.35 where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S. News and World…

The cost of attending your college has once again gone up. Although you have been told that education is investment in human capital, which carries a return of roughly 10% a year, you (and your parents) are not pleased. One of the administrators at your university/college does not make the situation better by telling you that you pay more because the reputation of your institution is better than that of others. To investigate this hypothesis, you collect data randomly for 100 national universities and liberal arts colleges from the 2000-2001 U.S. News and World Report annual rankings. Next you perform the following regression Cost = 7,311.17 +3,985.20 × Reputation - 0.20 × Size +8,406.79 x Dpriv-416.38 × Dlibart-2,376.51 x Dreligion (2,058.63) (664.58) (0.13) (2,154.85) R² = 0.72, SER = 3,773.35 where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S. News and World Report (based on a survey of university presidents and chief academic officers),…

Neurologists have found that the hippocampus, a structure located in the brain, plays an important role in short-term memory. Data was collected on 21 Vietnam veterans with combat related post-traumatic stress disorder. Magnetic resonance imaging was used to measure the volume of the right hippocampus (in cubic millimeters) of each subject, while the verbal memory retention of each subject was measured by the percent retention subscale of the Wechsler Memory Scale. The least squares line relating verbal memory (y) with right hippocampal volume (x) was found to be 4 + 3x. The slope of the regression line can be interpreted in the following way: ŷ = When right hippocampal volume decreases by one cubic millimeter, the verbal memory score increases by 3%. When right hippocampal volume decreases by one cubic millimeter, the verbal memory score increases by 4%. When right hippocampal volume increases by one cubic millime decreases by 3%. the verbal memory score When right hippocampal volume…

Hyperhidrosis is a stressful medical condition characterized by chronic excessive sweating. Botox was approved for treatment of hyperhidrosis in adults in 2004. A clinical trial examined the effectiveness of Botox for excessive armpit sweating in teenagers aged 12 to 17 years. Participants received either a Botox injection or a placebo injection (a simple saline solution) and were examined four weeks later to see if their sweating had been reduced. Here are the study's findings: Botox Placebo Total Reduced Confidence Interval: 72 52 124 Not Reduced 28 We are 95% confident that there is hyperhidrosis who experienced a reduction in sweating. 148 176 Total 100 200 - Construct a 95% confidence interval for p₁ - P2 where p₁ denotes the proportion of teenagers who experienced a reduction in sweating in the Botox group and p2 denotes the proportion of teenagers who experienced a reduction in sweating in the placebo group. Round your answers to three decimal places, and use four decimal places…

A team of government researchers would like to determine whether a new tax on cigarettes has any effect on people’s smoking behavior. Specifically, they are expecting that by increasing the price of cigarettes, people’s will buy fewer packs of cigarettes (ultimately leading to decreases in cigarette smoking). During the year before the tax was imposed, stores located in rest areas on the state highways reported selling an average of µ = 410 packs per day. The distribution of daily sales was approximately normal. For a random sample of n = 25 days during the first year following the new tax, the researchers found an average of x̅= 380 packs per day for the same stores, with a standard deviation of s = 60. Is the sample mean sufficient to conclude that there was a significant decrease in cigarette purchases after the new tax? Use a one-tailed test with α = .01.

A certain training device measures reaction times of users by illuminating lights, one at a time, and measuring the time it takes the user to press each light to turn it off. The makers of the device are marketing it for high-level training, saying that even among professional athletes, the proportion who can score the top ranking of "light speed" is less than  22% . As a fitness trainer who wants to buy the device to attract more customers, you want to feel comfortable that the claim made by the makers is correct. To test the claim, you decide to perform a hypothesis test. To do so, you rent the device and have a random sample of  130  professional athletes use it;  26  score a ranking of "light speed."   You confirm that it is appropriate to perform a  Z -test. Why is a  Z -test appropriate?     Find  z , the value of the test statistic for your  Z -test. Round your answer to three or more decimal places. =z

A study published by Babcock and Marks (2010) showed that the average full-time U.S. college student studied for μ = 14 hours per week (SD = 4.8 hours per week) in 2005. We want to know if this average has changed in the past 15 years. In other words, we are going to do a study in which we try to determine whether there has been an impact of the passage of time on the amount of time college students spend studying. We selected a sample of n = 64 of today’s college students and find that they spent an average of M = 12.5 hours per week studying. Does this sample indicate a significant change in the number of hours spent studying? Use a two-tailed test (this means non-directional hypothesis) with α = .05.