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- Explain the Stationarity in the AR(1) Model?According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 5,000 roaches (the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 18,857 dead roaches were counted, a gain of 13,857 roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.4. Use the number of roaches produced by the sample of 5,000 roaches to find a 90% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. Find a 90% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. (Round to three decimal places as needed.)A study was conducted to assess the impact of nutrient enrichment on zooplankton densities in A & B Islands. An ecologist sampled populations of zooplankton in these two locations and observed the nutrient enrichment level was higher in A island when compared with the level in B island. It is predicted the zooplankton densities in A island will be greater than those found in B island.
- This exercise requires the use of technology.Four sectors of the U.S. economy are (1) livestock and livestock products, (2) other agricultural products, (3) forestry and fishery products, and (4) agricultural, forestry, and fishery services. Suppose that in 1977 the input-output table involving these four sectors was as follows (all figures are in millions of dollars).Determine how these four sectors would react to an increase in demand for livestock (Sector 1) of $1,000 million, how they would react to an increase in demand for other agricultural products (Sector 2) of $1,000 million, and so on. (Round your answers to two decimal places. Let the columns of the matrix be given in millions of dollars.) To 1 2 3 4 From 1 11,937 9 109 855 2 26,649 4,285 0 4,744 3 0 0 439 61 4 5,423 10,952 3,002 216 Total Output 97,795 120,594 14,642 47,473The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite as quickly. A cognitive psychologist is interested in whether cuttles exhibit learning (by showing a reduction in reaction time) after repeated exposure to the same environment. Initially, 10 baby cuttlefish are individually placed in a tank with a checkerboard bottom and their reaction time (time to camouflage) is recorded. Over the next month the samecuttlefish are exposed to the same environment daily and at the end of the month each cuttlefish's reaction time is recorded again. The data are recorded in the table below. Reaction Time (seconds) Subject Before After 1 58 41 2 48 45 3 54 40 4 56 42 5 55 48 6 55 41 7 43 32 8 51 44 9 62 38 10 35…A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.
- In a M/M/1 model, the average number of customers in the system is 16, and the average waiting time in the system (i.e., response time) is 53 minutes. Then, the average service time (in minutes) is 03.3125 03.11769 00.32075 00.30189In the production process of a company, 4 units of a certain input are used daily. It happens that the different formulations of this input can affect the yield of the process as well as the level of environmental pollution. On a given day the company has 40 units of this input in stock and they can be classified according to the table below:Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 pm with the meters off resulted in the following speeds (in miles per hour). (a) Uraw side-by-side Doxplots of each data set Does there appear to be a merence in the speeds? Are there any outlers? Choose the correct Dox plot below. A. 0 Off 15 30 45…
- Read the pages and make a summary of them with your own words, please. It is what you understand.Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal). The results were as follows: Duration of Exposure <1 1 to <5 ≥5 Diseased 14 13 18 Sensitized 11 20 15 Normal 78 140 209 Test the hypothesis of independence. Use the a=0.10 level of significance and the P-value method with the TI-84 Plus calculator. What do you conclude? State the null and alternate hypotheses.Assume a single server queueing system with exponential inter-arrival times, and service times. Assume that the expected inter-arrival time is 10 minutes, and the expected service time is 7.5 minutes. We are interested in the expected time the customers spend waiting in queue (in minutes). Develop a Monte Carlo simulation model to estimate Wg Calculate W (expected wait time in queue), and compare it with the previous result
