Chapter 11: Inference for a Normal Population - 8 points 6. Global warming is causing many species living on mountain slopes to shift their elevational ranges upward. Is the vertical extent of their ranges (the difference betw e between the upper limit and the lower limit of their elevational range) also changing as ranges shift upward? To examine this, Freeman et al. (2018) surveyed birds on the Cerro de Pantiacolla in Peru in 2017 and compared their findings to a previous survey of the same mountain in 1985. The following numbers are changes in the vertical range extent of 14 mid-elevation bird species, in meters. A negative number indicates that the vertical extent of the range of that species has decreased, whereas a positive number indicates an increase; 0 indicates no change. 100, 380, -100, 0, -50, -50, -50, -150, 100, -50, -50, -200, 50, 100 a. Test the null hypothesis that the mean change in the vertical extent of mountain birds is 0 meters (i.e., is neither increasing nor declining but is stable in the face of global warming). 2 points b. What changes in the vertical extent of range are nevertheless consistent with the data? To answer, calculate the 95% confidence interval for the change in vertical range. 2 points 7. Male koalas bellow during the breeding season, but do females pay attention? Charlton et al. (2012) measured responses of estrous female koalas to playbacks of bellows that had been modified on the computer to simulate male callers of different body size. Females were placed one at a time into an enclosure while loudspeakers played bellows simulating a larger male on one side (randomly chosen) and a smaller male on the other side. Male bellows were played repeatedly, alternating between sides, over 10 minutes. Females often turned to look in the direction of a loudspeaker (invisible to her) during a trial. The following data measure the preference of each of 15 females for the simulated sound of the "larger" male. Preference was calculated as the number of looks toward the larger-male side minus the number of looks to the smaller-male side. Preference is positive if a female looked most often toward the larger male, and it is negative if she looked most often in the direction of the smaller male. Data: -2, 2, 6, 9, 13, 2, 5, 7, 2, -6, 4, 3, 2, 6, -6 5 - 4- Frequency 3- N -10 5 10 15 Preference for larger-male sound a. Do females pay attention to body size cues in simulated male sounds? Carry out a test, making all necessary assumptions. Explain what all of the components in the test output mean, as they relate to these data. 4 points2. In animals without paternal care, the number of offspring sired by a male increases as the number of females he mates with increases. This fact has driven the evolution of multiple matings in the males of many species. It is less obvious why females mate multiple times, because it would seem that the number of offspring that a female has would be limited by her resources and not by the number of her mates, as long as she has at least one mate. To look for advantages of multiple mating, a study of the Gunnison's prairie dog followed females to find out how many times they mated (Hoogland 1998). They then followed the same females to discover whether they gave birth later. The researchers wanted to know if the number of times a female mated affected her probability of giving birth. Use the information in the following table to answer questions a-e below: Number of times female mated: 1 2 3 4 5 Number who gave birth 77 86 61 17 5 Number who didn't give birth 10 7 0 0 0 a. State the null and alternative hypothesis for this study; be sure to include the expected frequency value (Po) in your hypotheses. 2 points Null: Alternative: b. Calculate the expected frequencies. 2 points 5 Row 2 totals Number who gave birth Number who didn't give birth Column totals 263e. What is the relative risk for female Gunnison's prairie dogs of not giving birth if they mate more than once - explain what this means? 2 points