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Chapter 4 110 ASSIGNMENT PROBLEMS tides. 15. A massive survey of sexual attitudes and behav- statem ior in Britain between 1999 and 2001 contacted a. Th 16,998 households and interviewed 11, 161 is respondents aged 16-44 years (one per respond- b. Th ing household). The frequency distributions of is ages of men and women respondents were the C. Th same. The following results were reported on tic the number of heterosexual partners individuals d. A had had over the previous five-year period lil (Johnson et al. 2001). to Sample Standard p size, n Mean deviation Men 4620 3.8 6.7 17. The Women 6228 2.4 4.6 a U.S displ a. What is the standard error of the mean in 95% men? What is it in women? Assume that the subs sampling was random. expl b. Which is a better descriptor of the variation 2.0 among men in the number of sexual partners, actu the standard deviation or the standard error? char Why ? it is c. Which is a better descriptor of uncertainty pret in the estimated mean number of partners in women, the standard deviation or the stan- dard error? Why? d. A mysterious result of the study is the dis- crepancy between the mean number of part- ners of heterosexual men and women. If each Concentration sex obtains its partners from the other sex, then the true mean number of heterosexual partners should be identical. Considering aspects of the study design, suggest an expla nation for the discrepancy. 16. Our unique random sample of 100 human genes from the human genome (Example 4.1) was found to have a median length of 2150 nucleo- 18. Amo West 7. Redrawn from a figure at http://www.pnl.gov/env/Helpful2.html. Acce flowConcentration O - NW A UT 2 W - Substance 18. Amorphophallus johnsonii is a plant growing in West Africa, and it is better known as a "corpse- flower." Its common name comes from the fact ful2.html. Accessed January 15, 2006.that when it flowers, it gives off a "powerful aroma of rotting fish and faeces" (Beath 1996). 140 The flowers smell this way because their prin- 120 - cipal pollinators are carrion beetles, who are 100 attracted to such a smell. Beath (1996) observed 80 the number of carrion beetles (Phaeochrous A. 60 - amplus) that arrive per night to flowers of this 40 species. The data are as follows: 20 - 51, 45, 61, 76, 11, 117, 7, 132, 52, 149 0 - a. What is the mean and standard deviation of beetles per flower? b. What is the standard error of this estimate of 2000 - the mean? c. Give an approximate 95% confidence inter- 1500 val of the mean. Provide lower and upper B. 1000 limits. d. If you had been given 25 data points instead 500 of 10, would you expect the mean to be 0- greater, less than, or about the same as the mean of this sample? e. If you had been given 25 data points instead of 10, would you have expected the standard 200 deviation to be greater, less than, or about the same as this sample? 150 f. If you had been given 25 data points instead of 10, would you have expected the standard C. 100 error of the mean to be greater, less than, or 50 about the same as this sample? 19. The following three histograms (A, B, and C) 0 plot information about the number of hours of sleep adult Europeans get per night (Roenneberg 2012). One of them shows the frequency distri- a. Ider bution of individual values in a random sample. dist b. Wh for sam Another shows the distribution of sample means you samef. If you lau instead of 10, would you have expected the standard C. error of the mean to be greater, less than, or about the same as this sample? 19. The following three histograms (A, B, and C) plot information about the number of hours of sleep adult Europeans get per night (Roenneberg 2012). One of them shows the frequency distri- bution of individual values in a random sample. Another shows the distribution of sample means for samples of size 10 taken from the same population. Another shows the distribution of sample means for samples of size 100.Assignment Problems 111 140 - 120 100 ed 80 A. 60 40 20 49 O 5 6 7 8 9 10 11 of 2000 1500 B. 1000 500 5 6 7 8 9 10 11 P rd 200 - the 150 - d rd C. 100 r 50 - 0 8 9 10 11 erg i- a. Identify which graph goes with which le. distribution. ans b. What features of these distributions allowed you to distinguish which was which? c. Estimate by eye the approximate population mean of the number of hours of sleep using the distribution for the data. d. Estimate by eye the approximate mean of the distributions of sample means.d. Estillia for the mean activity ( un ral sandpipers. Using this smallest plausible value, calculate approximately the maximum plausible number of hours (out of 24 hours) that males spend inactive or asleep. 22. How long do you hug somebody? Nagy (2011) measured the duration of spontaneous embraces at the 2008 Summer Olympic Games in Beijing, China. The data are the durations of hugs, in seconds, of athletes immediately after compet- ing in the finals of an event. Hugs were either with their coach, a supporter (e.g., a team mem- ber), or a competitor. Descriptive statistics cal- ble culated from the data are in the following table. n refers to the sample size. et al. Standard reed- Relationship Mean deviation n oS) Coach 3.77 3.96 77 n Supporter 3.16 2.76 75 vs the Competitor 1.81 1.13 33 es dy. The a. According to the values in the table, which a are relationship group gets the longest hugs, on bars average, and which gets the briefest hugs? ror ofduration? f. For which of the relationship groups is the possibility of a 3-second mean hug duration in the population plausible? 23. Pitcher plants of the genus Nepenthes are typi- cally carnivorous, obtaining a great deal of their nutrition from insects that become trapped in the pitcher, die, and decay. N. lowii, a pitcher plant from Borneo, produces a second type of pitcher that attracts tree shrews (Tupaia mon- tana), which provide nutrients by defecating into the pitcher 8 while they feed on a substance secreted by the plant. Based on measurements of 20 plants, Clarke et al. (2009) calculated a 95% confidence interval for the mean fraction of total leaf nitrogen in the plant species derived from tree shrews: 0.57
