c. What is the probability that the first diameter is between 4 and 6 and the second diameter is between 8 and 12? d. What is the probability that the first diameter is between 8 and 12 or the second diameter is between 10 and 12? Chapter 6: Hypothesis Testing 4. State the most appropriate null and alternative hypotheses for each of the following experiments or observational studies (3 points). a. A test of whether Pygmy mammoths and continental mammoths differ in their mean femur lengths. Null: Alternative: b. An experiment to test whether mean herbivore damage to a genetically modified crop plant differs from that in the related unmodified crop Null: Alternative: 5. Identify whether each of the following is more appropriate as a null hypothesis or an alternative hypothesis. Explain. (2 points) a. Industrial effluents from a factory into the Mississippi River negatively affect the downstream fish densities b. King cheetahs on average run the same speed as standard spotted cheetahs.3. The figure below shows the probability density of colony diameters (in mm) in a hypothetical population of Paenibacillus bacteria. The distribution is continuous, so the probability of sampling a colony within some range of diameter values is given by the area under the curve. Numbers next to the curve indicate the area of the region indicated in red. Consider the case in which two colonies are randomly sampled from the probability distribution shown. 2 points total (1/2 point per a, b, c, and d) 0.4 7 0.4 7 0.3 0.14 0.3 - 0.14 Probability density 0.2 0.2 - 0.1 - 0.1 O 8 10 12 14 2 4 6 8 10 12 14 0.4 7 0.47 0.3 - 0.48 0.3 Probability density 0.2 0.2 0.1 - 0.1 - 0.02 o 2 6 8 10 12 14 6 8 10 12 14 Colony diameter (mm) Colony diameter (mm) Whitlock & Schluter, The Analysis of Biological Data, 3e @ 2020 W. H. Freeman and Company a. Are the events "the first diameter is between 4 and 6" and "the second diameter is between 8 and 12" mutually exclusive? Explain. b. Are the events "the first diameter is between 4 and 6" and "the second diameter is between 8 and 12" independent? Explain.Chapter 5: Probability 1. The human genome is composed of the four DNA nucleotides: A, T, G, and C. Some regions of the human genome are extremely G-C rich (i.e., a high proportion of the DNA nucleotides there are guanine and cytosine). Other regions are relatively A-T rich (i.e., a high proportion of the DNA nucleotides there are adenine and thymine). Imagine that you want to compare nucleotide sequences from two regions of the genome. Sixty percent of the nucleotides in the first region are G-C (30% each of guanine and cytosine) and 40% are A-T (20% each of adenine and thymine). The second region has 25% of each of the four nucleotides. 4 points total (2 points for part a and 2 points for part b) a. If you choose a single nucleotide at random from each of the two regions, what is the probability that they are the same nucleotide? Show your calculations, making your answer clear (by highlighting or bolding; if done in R, feel free to screenshot your Code in the box below) b. Assume that nucleotides over a single strand of DNA occur independently within regions and that you randomly sample a three-nucleotide sequence from each of the two regions. What is the chance that these two triplets are the same? Explain how you determined this. 2. A seed randomly blows around a complex habitat. It may land on any of three different soil types: a high-quality soil that gives a 0.8 chance of seed survival, a medium-quality soil that gives a 0.3 chance of survival, and a low-quality soil that gives only a 0.1 chance of survival. These three soil types (high, medium, and low) are present in the habitat in proportions of 30:20:50, respectively. The probability that a seed lands on a particular soil type is proportional to the frequency of that type in the habitat. 4 points total a. Draw a probability tree to determine the probabilities of survival under all possible circumstances. 2 points. You may take a picture and load it into the box, or build your tree as started below: Survive 0.8 High-Quality Soil b. What is the probability of survival of the seed, assuming that it lands? 1 point c. Assume that the seed has a 0.2 chance of dying before it lands in a habitat. What is its overall probability of survival? 1 point