Determine whether (5) () = (;) (") n-3 (where 3 < k < n) is true or %3D false. O True O False
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- If H1: μ1 – μ0 < 0, then zobs = -1 has a lower p-value than zobs =1. True or false?Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same asA manufacturer of pins knows that 5% of his product is defective. If he sells pins inboxes of 100 and guarantees that not more than 4 pins will be defective. What is theprobability that a box will fail to meet the guaranteed quality?
- on solution 3 the probablity that tails would appear on both coins is 14?(!) In the morning section of a calculus course, 2 of the 9 women and 2 of the 10 men receive the grade of A. In the afternoon section, 6 of the 9 women and 9 of the 14 men receive A. Verify that, in each section, a higher proportion of women than of men receive A, but that, in the combined course, a lower proportion of women than of men receive A. Explain!When the health dept. tested private wells in a county for 2 impurities commonly found in drinking water, it found that 20% of the wells had neither impurity, 30% had impurity A, 40% had impurity B, and 10% had both impurities. If 20 wells are randomly inspected from those in the county, find the prob. that 10 had neither impurity, 4 had impurity A, 4 had impurity B,and 2 had both impurities (rounded odd to 4 decimal places).. A. 0.0001 B. 0.1011 C. 0.2900 D. 0.9990
- A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=3,Y=4).Even though you have no symptoms, your doctor withes to test you for a raredisease that only 1 in 10,000 people of your age contract. The test is 98%accurate, which means that, if you have the disease, 98% of the times the testwill come out positive and 2% negative. Also, if you do not have the disease, the test will come out negative 96% of the time and positive 4% of the time. You take the test and it comes out positive. What is the probability that you have the disease?What is the purpose of testing whether ᵝ1=0? If we reject ᵝ1=0, does it imply a good fit?
- Suppose now that you have good arguments to say that the association between X andC (the unobserved confounding factor, here IQ at age 3), measured by γCX, is of a similarmagnitude as the association between X and A, measured by γAX — which you can computein your data (since A is observed). Would this new condition (γCX = γAX). Why?In a recent study, 50males used a new weight-loss supplement, and 38 of them experienced weight loss after two weeks. In the same study, 20 females used the same supplement, and 16of them experienced weight loss after two weeks.Fill in t he blanks below to make the most reasonable statement possible. The new weight-loss supplement was less effective on ▼(Choose one: males/females) in the study. That is because only ____% of them lost weight after two weeks, whereas ____% of the ▼(Choose one:males/females) lost weight after two weeks.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?
