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- In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normalFrom historical data at a local restaurant indicate that 60% of customers order coffee, 15% order soft drinks, and the remaining order water. The owner of the restaurant is planning on opening a new restaurant for the purpose of stocking enough of various drinks, wants to know if the proportions are the same for his new restaurant as they were for his original restaurant. In a sample of 1000 customers at the new restaurant, 550 ordered coffee, 190 order soft drinks, and the remaining simply wanted water. At the 5% level of significance, does it appear the proportions have changed?An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 3% of the microprocessors produced by firm A are defective, 4% of those produced by firm B are defective, and 1.5% of those produced by firm C are defective. Firms A, B, and C supply 35%, 20%, and 45%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?
- At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B Consider a random sample of n=9 people who donated blood over the past three months. a) The expected number of people with blood type O+ is _____and the expected number of people with blood type A- is ______Round your answers to 2 decimal places. b) Calculate the following probabilities: P(X=5)=_________ Round your answer to 4 decimal places. P(X>2)=_________ Round your answer to 4 decimal places.If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries. a) unlikely to have b) very unlikely to have c) guaranteed to have d) guaranteed to not haveSuppose 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…A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 10 cars, chosen at random. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Brand 1 0.54 0.62 0.37 0.42 0.58 0.50 0.53 0.64 0.53 0.40 Brand 2 0.39 0.33 0.33 0.33 0.28 0.46 0.29 0.55 0.45 0.37 Difference(Brand 1 - Brand 2) 0.15 0.29 0.04 0.09 0.30 0.04 0.24…A certain process for manufacturing integrated circuits has been in use for a period of time, and it is known that 12% of the circuits it produces are defective. A new process that is supposed to reduce the proportion of defectives is being tested. In a simple random sample of 100 circuits produced by the new process, 12 were defective. a) One of the engineers suggests that the test proves that the new process is no better than the old process, since the proportion of defectives in the sample is the same. Is this conclusion justified? Explain. b) Assume that there had been only 11 defective circuits in the sample of 100. Would this have proven that the new process is better? Explain. c) Which outcome represents stronger evidence that the new process is better: finding 11 defective circuits in the sample, or finding 2 defective circuits in the sample?
- At the Blood Bank, they know that O+ blood is the most common blood type and that 40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6% of the people have A- blood. Half of the people have blood type A or B. Let: X= number of people who have blood type O+ Y= number of people who have blood type A- Z= number of people who have blood type A or B a) Consider a random sample of n=9 people who donated blood over the past three months. The expected number of people with blood type O+ is and the expected number of people with blood type A- is Calculate the following probabilities: P(X=5)= __________ Round your answer to 4 decimal places. P(X>2)= __________ Round your answer to 4 decimal places. b) Consider a random sample of n=40 people who donated blood over the past three months. Use the relevant probability function of Y to calculate the probability that 2 people in the random sample will have type A- blood. ________…A production manager is interested to know if the distribution of defective items produced by threemachines are homogeneous. From a random sample of 200 items produced by machine I it wasfound that 150 items have no falt, 30 items have one fault and rest of the items have more than onefault. Of the 180 items produced by the machine II it was found that 85% items have no fault, 10%items have one fault and rest of the items have more than one fault. From a total of 220 itemsproduced by machin III, it was found that 205 items have no fault, 10 items have one fault and restof the items have more than one fault.(a) Construct the contigency table considering status of defectives in row and type of machinein column(b) What percentage items with one fault produced by each of the machine I and III?(c) Test at 5% significance level whether the distribution of defective items produced by threemachines are homogeneous or not?At pandemic time of COVID 19 surveys are conducted in two townships which fall into the same Lusaka city. In Chawama, 175 tested positive out of a sample of 318 who were tested for COVID 19. In Kabulonga, 143 tested positive out of a sample of 307 who were tested for COVID 19. At the 5% level, is there a difference between the proportions of those who tested positive in each area
