The virus DIVOC-91 has been infecting the residents of the Moniyan Empire. lowever, due to the diligence of their queen, the virus has been contained within Moniyan only. Researches found out that the number of infected residents in thousands after t months is given by 6t2 p(t) = 0.15t3 - 0.1t +0.5" Will the number of infected individuals zero out eventually and will the Moniyan Empire be free from the virus? Justify using limit concepts.
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- A group of investigators wishes to explore the relationship between the use of hair dyes and the development of breast cancer in females. A group of 100 beauticians 40–49 years of age is identified and followed for five years. After five years, 20 new cases of breast cancer have occurred. Assume that breast cancer incidence over this time period for average American women in this age group is 30/100. We wish to test the hypothesis that using hair dyes decrease the risk of breast cancer. Compute p-value (The answer is Not 0.0021) Please choose answer from these two following multiple choice. a) 0 b) 47.6190An article published in the American Journal of Hypertension reported the results of a longitudinal study on blood pressure. Ten years ago, 51 out of 188 people evaluated were classified as having high blood pressure. This year, 63, out of 194 people evaluated were classified as having high blood pressure. Based on the results of this study, can one conclude that the proportion of people in the population with high blood pressure has increased in the last ten years? Use a = 0.05. I can't find the sign=a I hope someone will know what I am talking about.A statistics professor bought a new car for $35,000. For the next 5 years, she used several automotive web pages to estimate the value of the car. She then found the least‑squares regression line for the data to be y^ =35035.71−4142.86x where yy is the value of the car and xx is the years since she purchased it. Predict the value of her vehicle after 6 years.
- A research study in a big metropolitan area shows that 2% of individuals living within the city limits move to suburbs during one-year period while 1% of individuals living in the suburbs move to the city during a one-year period. Define the approach that should be used to solve the problem and identify all your inputs of the model.The 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…Many runners believe that listening to music while running enhances their performance. The authors of a paper wondered if this is true for experienced runners. They recorded time to exhaustion for 11 triathletes while running on a treadmill at a speed determined to be near their peak running velocity. The time to exhaustion was recorded for each participant on two different days. On one day, each participant ran while listening to music that the runner selected as motivational. On a different day, each participant ran with no music playing. You can assume that it is reasonable to regard these 11 triathletes as representative of the population of experienced triathletes. Only summary quantities were given in the paper, but the data in the table below are consistent with the means and standard deviations given in the paper. Time to exhaustion (in seconds) Motivational music Runner 1 3 4 5 6 7 8 9 10 11 535 534 527 521 432 498 555 399 536 543 524 No music 467 449 483 574 563 593 474 499…
- You are an aerospace engineers designing the next generation of space shuttles that includes two engines —one active, the other in reserve. If the primary engines fails, the second is automatically brought on line. Suppose a typical mission is expected to require that engine to work at most 5000 hours. According to the manufacturer's specifications, engine are expected to fail once every 10000 hours. What are the chances that such engine system would not remain functioning for the full 5000 hours? Hint, Use Gamma Distribution.In laboratories where clinical tests are carried out, two types of test are available for the detection of a highly contagious virus. The Type A test is very fast and inexpensive while the Type B test is a test that requires more time to obtain a diagnosis and is more expensive. It is known that the economic test. Type A, generates correct diagnosis (C) in 60% of cases. While the Type B test provides the correct diagnosis (C) in 99% of cases. If after six months of quarantine due to this virus the health secretary realizes that 80% of the tests carried out in the state correspond to Type A economic tests and only 20% were Type B. If it is known that a test made an incorrect diagnosis. What is the probability that the Type A economic test did? .9937 .24844 .322 .6211 .3788Imagine you need to come up with a diagnostic test to monitor the viral load of patients with HIV. If the viral load is higher than a set standard, there is evidence the anti-retroviral therapy is no longer working and the patient needs to be moved to a different therapy that costs more money. Thus, false positives incur higher costs. However, if the test misses higher than normal viral loads (for patients in treatment), then the patient runs the risk of developing AIDS. Hence, false negatives result in a likely deadly disease. How would you balance these two types of error in devising your test? Minimize beta by raising the one-tailed alpha, since greater power will reduce false negatives and save patients O Minimize the one-tailed alpha, since lower P-values indicate the test is highly significant and prevent prematurely switching the patients Minimize the one-tailed alpha and beta, since this action will prevent prematurely switching the patients and reduce false negatives, thereby…
- In 2004 it was reported that 31% of all graduating US college students were graduating with STEM degrees (Science Technology Engineering and Math). You want to study if this percentage has increased. To study this you divide the country into 4 major regions, East Coast, Midwest, South, and West Coast and randomly sample 70 students from each region. This means you ultimately randomly sample 280 graduating students and find that 95 of them were graduating with STEM degrees. (a) Carry out at α = .05 a hypothesis test to test the claim that the percentage of US college students that get STEM degrees has increased since 2004. Make sure to check all necessary condi- tions and state your conclusion in the context of this problem. (b) Build a 95% confidence interval to estimate the current percentage of US college students that graduate with a STEM degree. Make sure to check any necessary conditions and interpret your interval in the context of this problem. (c) What type of sampling did you…A headline on a news website stated “Sheep with a varied diet grew faster and produced less pollutants, new study finds.” The article reports that scientists using pregnant sheep that were twin-bearing to test how diet affected the lambs. When the twin lambs were born, one lamb was put on a typical rye grass diet, while the other was given a variety of feeds, including chicory, plantain, red clover and lucerne. The impact was huge, with the lambs given a variety of feeds seeing a 100 per cent increase in growth, excreted less nitrogen into the environment and had an improved well-being.Describe in one or two sentences what is the explanatory variable and what are the response variables mentioned in this study.Suppose you have a survey where one of the variables is "Sex", and all of the 300 people surveyed answered one of the following: 1) Male or 2) Female. Suppose further that you create 2 dummy variables: D1 = 1 if male, zero otherwise D2 = 1 if female, zero otherwise What would happen if you include both dummy variables in your regression in Excel? O Excel will not be able to run a regression with both variables in the regression. Nothing. This is the correct way to do it. O Your regression will exhibit serial correlation. O Your regression will exhibit some multicollinearity, but can be remedied with "robust standard errors."