1. For each of the following - describe the most appropriate statistical test you should use for the experimental design and why (we may not have discussed all of the tests by recitation period - but you will need to be familiar with each for the 3" exam). You collect blood pressure values for a group of people before swimming with sharks and then blood pressure values from the same group of people after swimming with sharks, looking to see if blood pressure changes before and after. You use flow cytometry to assess the effects of a drug on cell death - you count the number of live cells, early apoptotic cells (early-stage of cell death), late apoptotic cells, and dead cells and compare it to the expected ratio of these cell types which are normally found in a 2:1:1:1 ratio. We gather 20 pairs of twins, assign half of the sets of pairs to an exercise regime and the other half of the sets of pairs to a diet regime, and then compare the amount of weight they lose. You collect a sample of frogs and count the number of spots that they have on their bodies. You compare the average number of spots to your expected number of 23 spots per frog. You are interested in the predatory behavior of damselfly larvae on mosquito and aquatic beetle larvae in tree holes in Panama. You count the number of mosquito larvae and aquatic beetle larvae in tree holes when damselflies are present and absent. 2. There are many claims that eating organic food leads to better health outcomes. To study this, a dietician collects data from her patients: she categorizes their blood pressure values into elevated and healthy and she administers a questionnaire from which she can classify their diet into high in organic food and low in organic food. The data are shown in the table below. Healthy blood pressure Elevated blood pressure High organic diet 74 33 Low organic diet 395 267 Can you appropriately calculate the Chi-square value using these categories - why or why not? If you can, what is the Chi-square value for these data and would you reject the null hypothesis with this value (either use R or compare to the critical value). If you cannot, use the Fisher's Exact test (in R) to determine if you should reject the null hypothesis. 3. Which of the following is a property of the normal distribution [Check all that apply]? It is a continuous distribution It is bimodal It is skewed right It is centered at its mean 4. Explain how the standard deviation is related to the normal distribution. 5. The Z-distribution standardizes any normal distribution to make it easier to interpret if the mean value you obtained from your sample is comparable to what you would expect from the population. However, because you need to know the population standard deviation, it's not really feasible to use. What should you use instead, and why? 6. Consider a situation in which Rosa measures the diameter of 15 trees from a population that she thinks (based on published reports) has an average diameter of 240 cm. Her sample has a mean of 253.1 cm with a standard deviation of 25.21 cm. If she conducts a one-sample t-test of her data, what t-value would she obtain? Based on her t-test statistic, and the table of critical t- values shown below, which of the following P-value ranges matches the one for the t-value she obtains? 7. Use the information below and evaluate what type of statistical test you should use for these data and then conduct the appropriate test in R, interpreting your results. A group of researchers were interested in the effects of litter removal and addition on soil moisture content. They randomly selected 8 forest plots and then removed all litter from one half of the plot and added the removed litter on the other half of the plot. They measured the moisture content on each side of the plot, comparing the differences between them. Forest Plot Litter Removal Side Litter Addition Side Difference 0.15 0.30 -0.15 0.31 0.39 -0.08 C N 0.05 0.14 -0.09 4 0.11 0.21 -0.10 5 0.21 0.29 -0.08 6 0.17 0.20 -0.03 7 0.22 0.24 -0.02 8 0.12 0.09 0.03 8. Fiddler crabs use one of their claws as a mating display and one for feeding. Which claw is larger is thought to be equally likely, so we expect to see equal numbers of right-handed and left-handed crabs. Consider a survey of 30 crabs, which reveals 20 with larger right claws and10 with larger left claws. Calculate the X" value, and using the table of critical values for 1 degree of freedom shown, what is the conclusion of our test? Sig. level Value 0.05 3.84 0.025 5.02 0.01 6.63 9. Use the "Loading a .csv file into R instructions" section of the R functions document (should be uploaded to Course Materials by March 20" at the latest) to perform the Chi-square contingency analysis on the TV and aggression data set. Attach your mosaic plot and output results below