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- 3. A newly graduate of administration of justice has been hired by the regional director of the FBI to take a poll of a residential area to determine the proportion of residents who would be opposed to a gun exchange program in their community. The regional director of the FBI told her that if 50% or more of the residents are opposed to the idea, a gun exchange program will not be implemented. She takes a random sample of 150 household heads in the community and find that .42 of those sampled are opposed to the idea. Build a 99% confidence interval around this point estimate. Is 50% within her interval? What would she advise the regional director of the FBI who hired her?2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…. List the 10 possible samples (without replacement) of size 2 that can be obtained from the population of five officials. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) b. If a simple random sampling procedure is used to obtain a sample of two officials, what are the chances that it is the first sample on your list in part (a)? the secondsample? the tenth sample?
- Charlie will perform a hypothesis test at the a = 0.05 level. Felice will perform the same test at the a = 0.01 level.2) A local home inspector wants to test for lead levels in 10 homes using two different testing methods in each of the homes to determine the level of lead in each of the homes. Two different tests (A and B) are used to determine the level of lead found in each of ten randomly selected homes. The home inspector believes that Test A is more accurate than Test B. The data obtained, for lead level in each home using each method is shown in the table below. SPECIMEN 8| 9 2 3 4 6 7 10 A 22.7 23.6 24.0 26.6 27.2 28.7 35.0 32.5 44.1 47.3 Test B 23.0 23.2 23.5 25.6 27 27.1 33.2 35.3 40.5 47.8 a. Does this data provide convincing evidence to support the home inspectors claim? Provide a statistical justification to support your answer. b. What kind of error could you have made? What is one consequence of that error? c. Is the sample statistically significant at the 0.05 level? If not, at what significance level would these results be statistically significant at?Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used.The following table gives the percent of a country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively. Blood Types A+ A− B+ B− AB+ AB− O+ O− Percent 35.7 6.1 8.5 1.5 3.4 0.8 37.4 6.6 (a) What is the probability that a person selected at random from the population has a blood type that is type AB given that the person is Rh+? (Round your answer to two decimal places.)(b) What is the probability that a person selected at random from the population has a blood type that is Rh− given that the person is type O? (Round your answer to two decimal places.)
- 5.5. A distributed system contains 4 computers. What is the probability of its failure in one year, if probability of failure of the computers in this period are 0.1, 0.2, 0.3, 0.4?2. According to World Health Organization (WHO), the recommended limit for a noise level inside a classroom is 35 dBA. However, nine out of ten schools fail to meet this recommendation. A researcher wishes to conduct a study relevant to the prior information, but as a gap, he decides to include the area (in square meters) of every classroom and how it could possibly affect the resulting noise level. He selects 17 classrooms at random, and the noise levels are recorded in the next slide. a. Find the regression equation and construct the scatter plot diagram. b. Predict the noise level if a classroom has an area of 85.97 m². c. Calculate the coefficient of determination and interpret the findings. d. Calculate the coefficient of alienation and interpret the findings.
- 10. The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting 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 American population, what would the null and alternative hypotheses be? a. Ho: b. Ha2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used. The following table gives the percent of a country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or -, respectively. 0 Blood Types Percent A+ A 6.3 35.7 B+ B 8.5 1.5 AB+ AB 3.4 0.8 0+ 37.2 (a) What is the probability that a person selected at random from the population has a blood type that is type A given that the person is Rh? (Round your answer to two decimal places.) 6.6 (b) What is the probability that a person selected at random from the population has a blood type that is Rh* given that the person is type B? (Round your answer to two decimal places.)
