1. The article “Daily Weigh-Ins Can Help You Keep Off Lost Pounds, Experts Say,” (Associated Press, October 17, 2005) describes an experiment in which 291 people who had lost at least 10% of their body weight in a medical weight-loss program were assigned at random to one of three groups for follow-up. One group met monthly in person, one group met monthly in an online chat room, and one group received a monthly newsletter by mail. After 18 months, participants in each group were classified according to whether or not they had regained more than 5 pounds, according to the table below.
a. What is the expected number of participants who met in-person and regained 5 pounds or less?
b. The researchers wanted to determine whether the type of follow-up group is associated with the amount of weight regained. Write the appropriate null and alternative hypotheses.
c. What are the degrees of freedom for the test?
d. If using � = 0.01, what is the critical value of the test, according to the �! table?
e. Report the test statistic and �-value for the test. What conclusion can you draw?
Regained � lbs or Less Regained More than � lbs In-Person 52 45 Online 44 53 Newsletter 27 70
2. The article “Genetic Tweak Turns Promiscuous Animals into Loyal Mates” (Los Angeles Times, June 17, 2004) summarizes a research study that appeared in the June 2004 issue of Nature. In this study, 11 male meadow voles that had a single gene introduced into a specific part of the brain were compared to 20 male meadow voles that did not undergo the genetic manipulation. All of the voles were paired with a receptive female partner for 24-hours. At the end of the 24-hour period, the male was placed in a situation where he could either choose the partner from the previous 24-hours or a different female. The percentage of the time that the male spent with his previous partner during a 3-hour time period was recorded and the data is presented below.
a. Using � = 0.05, is there evidence to suggest that the population variances for the genetically modified group versus the unmodified group are equal? Report the test statistic and the �-value?
b. Based on the results of Part a, which will be more appropriate for comparing the mean percentage of the 3-hour period spent with the first female partner, the pooled estimate of variance or the Satterthwaite estimate of the degrees of freedom? Explain.
c. Using � = 0.05, do the genetically modified voles spend a different percentage of a 3-hour period with the first female partner when compared to the unmodified voles? Report the appropriate test statistic and �-value.
Genetically Altered: 59, 62, 73, 80, 84, 85, 89, 92, 92, 93, 100
Not Genetically Altered: 2, 5, 13, 28, 34, 40, 48, 50, 51, 54, 60, 67, 70, 76, 81, 84, 85, 92, 97, 99
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