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- What is the total effect on the economy of a government tax rebate of $500 to each household in order to stimulate the economy if each household will spend of the rebate in goods and services?A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?You are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. You conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each meal, asking that they simply check off that the meal was either satisfactory or unsatisfactory. For simplicity in this problem, assume that the response was 1,000 returned questionnaires from the 1,200 meals each day. The results are as follows: Day Number of Unsatisfactory Meals 1-Dec 74 2-Dec 42 3-Dec 64 4-Dec 80 5-Dec 40 6-Dec 50 7-Dec 65 8-Dec 70 9-Dec 40 10-Dec 75 a. Construct an appropriate control chart based on the questionnaire results, using two-sigma control limits. b. What comments can you make about the results of the survey? c. Show breakdown of computation/work.
- Suppose O1 is twice as likely as O4, O1 is equally as likely as O2, O5 is 5 times as likely as O2, and Pr[O3]=1/3. Find Pr[O5]The problem is "Twelve percent of the job applicants for a large company have recently smoked marijuana. The company gives all applicants a drug test. The test is not perfect. The test has a sensitivity of 98%- meaning that 98% of those who have recently smoked marijuana will test positive, the other 2% will test negative. The test has a specificity of 96%- meaning that if someone has not recently smoked marijuana, the test will correctly yield a negative test result 96% of the time." M = applicant has recently smoke marijuanaC= applicant has not recently smoked marijuana (clean)X = positive test (test indicates that the person has not recently smoked marijuana recently)N= negative test (test indicates that the person has not recently smoke marijuana) a. What proportion of those who test positive have not recently smoked marijuana? b. What proportion of those who pass the drug test really shouldn’t have?A foreign car manufacturer advertises that its newest model, the Bullet, rarely stops at gas stations. In fact, they claimed that its EPA rating for highway driving is at least 32.5 mpg. However, the results of a recent independent study determined the mpg for 50 identical models of the Bullet, with these results: n = 50, x= 30.4 mpg, and s = 5.3 mpg.This report failed to offer any conclusion, and you have been asked to interpret these results by someone who has always felt that the 32.5 figure is too high. What would be your conclusion using a significance level of 5%?Z = 1.645
- The problem is "Twelve percent of the job applicants for a large company have recently smoked marijuana. The company gives all applicants a drug test. The test is not perfect. The test has a sensitivity of 98%- meaning that 98% of those who have recently smoked marijuana will test positive, the other 2% will test negative. The test has a specificity of 96%- meaning that if someone has not recently smoked marijuana, the test will correctly yield a negative test result 96% of the time." M = applicant has recently smoke marijuana C= applicant has not recently smoked marijuana (clean) X = positive test (test indicates that the person has not recently smoked marijuana recently) N= negative test (test indicates that the person has not recently smoke marijuana) a. draw a tree diagram for this case b. What proportion of the applicants get an incorrect test result? c. What proportion of the applicants test positive?When Alexa takes her 1st free throw in a game, she has a 40 percent chance to score.She has a 70 percent chance of scoring on her next throw if she scored on the earlierone, but only a 20 percent chance if she didn't score on the previous one. Assumeshe needs to make 3 free throws in a row, the first of which she misses. What is theprobability that she will score at least once on one of the following two throws?A Company is planning a Children’s Christmas party for their 750 employees.Base on the survey responses they have 526 who indicated that they have girls and342 indicating that that have boys.From the survey how many possible employees have both boys and girls,if 75 employees did not do the survey?
- The burden of proof in civil cases is fairly low. A plaintiff wins a lawsuit if he is 51 percent convincing, and then he collects 100 percent of his damages. Is this result reasonable? Should a plaintiff in a civil case be required to prove his case beyond a reasonable doubt? Or, if a plaintiff is only 51 percent convincing, should he get only 51 percent of his damages?A researcher knows from decades of past research that scores on IQ tests have an average μ = 100. The researcher collects a sample of students from their own university and wants to know if the students they are studying are smarter than the average person based on past research. What test will they use to evaluate their hypothesis?If I had a p-value of < 2.2e-16, what is the scientific notation for this? Is this test significant? do I reject the null hypothesis?