Find the covariance between X and Y. Please provide the solution step by step.
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- Suppose that 95% of the bags of certain fertilizer mix weigh between 49 and 53 pounds. Averages of three succesive bags were plotted, and 47.5% of these were observed to lie between 51 and X pounds. Estimate the value of X. State assumptions you make and say whether these assumptions are likely to be true for this example.A motorcycle drives from Buendia to Quiapo and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Beundia to Quiapo and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by X y 1 2 3 4 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01Which option shows a positive linear association between the variables?
- A researcher is interested in studying how the number of books parents read to their children can influence a child's reading skills in kindergarten. She randomly assigns families with 5 year old children to either read their child 3 books per day, 2 book per day, or 1 book per day for the first 2 months of kindergarten. They then measure the children's reading ability. How could the confound be fixed for this scenario? Be sure to tell me what technique you are using (constancy, repeated measures, randomization, elimination, or balancing), as well as how you would apply that technique to this specific scenario, and how that would fix this confound.Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i 1,..., n.In this tab, we will run a statistical test to help us determine whether the bagworm is really preferring evergreen trees and shrubs over deciduous trees and shrubs. In this problem we are treating bagworm number as a continuous variable. Our statistical null hypothesis for this test is: The mean number of bagworms on evergreen trees will be the same as the mean number of bagworms on deciduous trees. Our statistical alternate hypothesis for this test is: The mean number of bagworms on evergreen trees will be different than the mean number of bagworms on deciduous trees. 1. Because you will be comparing the means of two groups and you are not specifying which direction the difference will be in, which test should you use? Highlight the correct answer below using the same color font you have been using for your other answers. i. Unpaired student’s t-test, one-tailed ii. Unpaired student's t-test, two-tailed iii. Paired student's t-test, one-tailed iv. Paired student's t-test, two-tailed…
