2. The effect of two factors---per-chamber volume ratio (V) and injection timing (T) on the parts per million of noxious gas emitted from an engine was studied. The volume ratio was set at three equi-spaced levels and the time was set at three equi-spaced levels. Two engines were built for each of the nine treatment combinations and the amount of the gas emitted was recorded for the 18 engines as shown in the Table. Time Volume (T) Low Medium High Short 6.27 8.08 7.34 5.43 Medium| 6.94 6.51 8.04 7.87 7.48 8.61 7.52 8.32 Long 7.22 8.65 9.02 7.05 8.97 9.07 a) Test the effect of volume b) Test the effect of time c) Test the effect of the interaction
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- One important aspect of medical diagnosis is its reproducibility. Suppose that two different doctors examine 100 patients for dyspnea in a respiratory-disease clinic and that doctor A diagnosed 15 patients as having dyspnea, doctor B diagnosed 10 patients as having dyspnea, and both doctor A and doctor B diagnosed 7 patients as having dyspnea. Compute the Kappa statistic and its standard error regarding reproducibility of the diagnosis of dyspnea in this clinic.A research focused on the number of illnesses involving the organism Escherichia coli (01257:H7), which causes a breakdown of red blood cells and intestinal hemorrhage in its victims. According to the Center for Disease Control of the Department of Health, an estimated 73,000 cases of E. coli infection and 61 deaths occur in Region Y. A 2028 outbreak traced to wild pigs, who spread the bacteria into a cabbage field in that , sickened 204 people in 26 municipalities. Outbreaks have occurred at a rate of 2.5 per 100,000. Let us suppose that this rate has not changed.a. What is the probability that at most five cases of E.coli per 100,000 are reported in California this year?b. What is the probability that more than five cases of E. coli are reported in California this year?c. Approximately 95% of occurrences of E. coli involve at most how many cases?According to U.S. government statistics, mononucleosis (mono) is four times more common among college students than the rest of the population. Blood tests for the disease are not 100% accurate. Assume that the following table of data was obtained regarding students who came to a certain school's health center complaining of tiredness, a sore throat, and slight fever. Has Mono Doesn't Have Mono Totals Positive Blood Test 19 44 63 Negative Blood Test 46 29 75 Totals 65 73 138 If a student is selected from this group, find the probability that the test is positive, given that the student has mono.
- A study of the characteristics of subcarriers—telecommunication signals carried on top of one another—for underwater acoustic communications was conducted. A sub-carrier can be classified as either a data subcarrier (used for data transmissions), a pilot subcarrier (used for channel estimation and synchronization), or a null subcarrier (used for direct current and guard banks transmitting no signal). In a sample of 1,024 subcarrier signals transmitted off the coast of Martha’s Vineyard, 672 were determined to be data subcarriers, 256 pilot subcarriers, and 96 null subcarriers. Suppose a communications engineer who works near Martha’s Vineyard believes that fewer than 70% of all subcarrier signals transmitted in the area are data subcarriers. Is there evidence to support this belief? Test using a significance level of .05. Write all steps.A neuroscientist hypothesizes that she found the region in the rat brain responsible for the motion of the right paw. She trains 20 right-handed rats in a specific task to push a lever to to receive a tasty pellet of food. After the all the rats learn the behavior, she randomly selects 10 of them a does a surgery to place an implant on the brains of rats through which a lazer can deactivate the said region in the brain. After the rats heal, she runs all the rats through the same task. While 10 of them went through the experiment unbothered, the other 10 who had the implant were stimulated by a lazer through their implants to disrupt the functioning of the hypothesized critical region. The neuroscientist collected the amount of rewards(number of food pellets received)the rats in both groups were able to collect:Xsurgery: 2, 4, 3, 1, 5, 3, 4, 1, 3, 4Xcontrol: 5, 6, 4, 6, 8, 9, 2, 5, 6, 3 c. Conduct the test. Make a decision about the null hypothesis, interpret your results and…A neuroscientist hypothesizes that she found the region in the rat brain responsible for the motion of the right paw. She trains 20 right-handed rats in a specific task to push a lever to to receive a tasty pellet of food. After the all the rats learn the behavior, she randomly selects 10 of them a does a surgery to place an implant on the brains of rats through which a lazer can deactivate the said region in the brain. After the rats heal, she runs all the rats through the same task. While 10 of them went through the experiment unbothered, the other 10 who had the implant were stimulated by a lazer through their implants to disrupt the functioning of the hypothesized critical region. The neuroscientist collected the amount of rewards(number of food pellets received)the rats in both groups were able to collect:Xsurgery: 2, 4, 3, 1, 5, 3, 4, 1, 3, 4Xcontrol: 5, 6, 4, 6, 8, 9, 2, 5, 6, 3 A. Name the appropriate statistical procedure to apply. B. Identify the predictor and predicted…
- In 20162016, the Chicago Cubs defeated the Cleveland Indians to become the champions of Major League Baseball. Following are the salaries, in millions of dollars, of the players on each of these teams. Cubs20.0012.009.508.808.057.755.695.293.632.672.532.512.500.650.540.530.530.520.520.520.510.510.510.510.51Cubs20.005.290.540.5112.003.630.530.519.502.670.530.518.802.530.520.518.052.510.527.752.500.525.690.650.51A geneticist working on peas has a single plant monohybrid Y/y (yellow) plant and, from a self of this plant,wants to produce a plant of genotype y/y to use as a tester. How many progeny plants need to be grown to be 95percent sure of obtaining at least one in the sample?An organization published an article stating that in any one-year period, approximately 11.5 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country. At a pre-conceived α = 0.05, what are your following?Decision: , Reason for the decision: ,Conclusion
- Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Set up an appropriate hypothesis to test whether or not the defect rate has increased. Before proceeding to test your hypothesis, check that all assumptions and conditions are satisfied for such a test. Conduct the test using a .05 level of significance (alpha) and state your decision about…Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Conduct the test using a .05 level of significance (alpha) and state your decision about whether or not you believe that the defect rate has increased. What would be the minimum number of defectives in a random sample of 1,000 would you need to find in order to statistically decide that the defect…An experiment was conducted to assess the effect of baking temperature on the density of bread. A large batch ofwhite bread dough and a large batch of whole wheat bread dough were prepared. Each of the batches was formedinto loaves, resulting in a total of loaves. Each of the white bread loaves was randomly assigned to one ofthree baking temperatures (low, medium, and high), so that loaves were baked at the low temperature, werebaked at the medium temperature, and were baked at the high temperature. A similar process of randomassignment was carried out for the whole wheat bread loaves.Which of the following are the treatments in the experiment? (A) The loaves of bread(B) The type of bread (white, whole wheat)(C) The density of the bread(D) The baking temperatures (low, medium, high)(E) The two batches of bread dough