Altigauge Manufacturing Company (AMC) makes 80% of all electrocardiograph machines, the Bryant Company (BC) makes 15% of them, and the Cardioid Company (CC) makes the remaining. The electrocardiograph machines made by AMC have a 4% rate of defects, the BC machines have a 6% rate of defects, and the CC machines have a 9% rate of defects. If a randomly selected electrocardiograph machine is tested and found to be defective, then what is the probability that it was made by AMC?
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9. The Altigauge Manufacturing Company (AMC) makes 80% of all electrocardiograph machines, the Bryant Company (BC) makes 15% of them, and the Cardioid Company (CC) makes the remaining. The electrocardiograph machines made by AMC have a 4% rate of defects, the BC machines have a 6% rate of defects, and the CC machines have a 9% rate of defects. If a randomly selected electrocardiograph machine is tested and found to be defective, then what is the probability that it was made by AMC?
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- 15. The U.S. Energy Information Administration claimed that in 2017, U.S. residential customers used an average of 10,399 kilowatt hours (kWh) of electricity. A local power company believes that residents in their area use more electricity on average than EIA’s reported average. To test their claim, the company chooses a random sample of 100 of their customers and calculates that these customers used an average of 10,608 kWh of electricity in the prior year. Assuming that the population standard deviation is 1361 kWh, is there sufficient evidence to support the power company’s claim at the 0.05 level of significance? (a) Symbolically, state the null and alternative hypothesis and state which is the claim. (b) Calculate the standardized test statistic. You must show a filled out standardized test statistic formula. (c) Find either the critical values and identify the rejection regions or find the p-value. Also, decide whether to reject or fail to reject the null hypothesis and be sure…9. A group of 50 single men were asked which dating apps they had on their phones. The follo data were collected: 33 of the men had the Tinder app. 30 of the men had the Coffee Meets Bagel app. 26 of the men had the Hinge app. 16 of the men had both the Tinder and Coffee Meets Bagel apps. 14 of the men had both Tinder and Hinge apps. 18 men had both Hinge and Coffee Meets Bagel apps. 7 men had all three apps on their phones. a) Represent this information in a Venn diagram: b) Calculate the number of single men who have none of these apps on their phone. c) How many single men only had Tinder on their phone? d) How many students own at most two of the apps?1. The percentage of 12- to 17-year-olds who reported talking at least once in the past year with their parents about the dangers of drug, tobacco, or alcohol is 60% nationally. A state youth council believes this proportion is higher in their state, where there has been an intense media campaign about this issue. A survey of randomly chosen students from across the state shows 1032 of 1642 students reporting they are having these conversations with their parents. Is there evidence that the percent of students using drugs, tobacco or alcohol in this state is above the national rate?
- 5. In recent years there has been a great deal of research demonstrating gender discrimination in science, technology, engineering and math (STEM) fields. In one experiment, for example, faculty members viewed an application for a laboratory manager position. The applications were identical except that half had a traditionally male name (John) and half had a traditionally female name (Jennifer). In addition, half of the faculty participants were from STEM fields and half were from non-STEM fields. The faculty were asked to rate the competence of the applicants on a 6-point scale, with 1 indicating a lower rating. Group means are presented below, along with an incomplete summary table. After completing the table, write a conclusion about the outcome of the experiment. Source Gender of applicant Male Female Between Treatments Gender of applicant Discipline of rater A x B interaction Within treatments Total SS 320 80 576 Discipline of Faculty Rater STEM M = 4.80 M = 4.02 df MS 20 1.25…6. To promote domestic consumption, Country A's government wants to determine the impact on household annual expenditures on consumption items if small stimulus checks were sent monthly over a one year period. To determine if these small stimulus checks would increase household expenditures on consumption items, it chose five households at random, determined their annual expenditure on consumption items for the year before and sent the stimulus checks for a year. The table below shows total amount of annual expenditure on consumption items by the households before and after receipt of the checks. Based on these observations, determine whether there would be a statistically significant difference in the mean annual expenditure on consumption items for the entire population of the Country A if this policy were adopted for the entire country. Use a level of significant of a = .01. Recipient 1 2 3 4 5 Before Receipt ($, in thousands) 63 38 70 65 62 After Receipt ($, in thousands) 65 42 68…7. A sociological study consists of recording the marital status, religion, race, and income of an individual. If marital status is classified into one of four categories, religion into one of three categories, race into one of five categories, and income into one of five categories, how many outcomes are possible for the experiment of recording the information of one of these individuals?
- 4. A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 200 house purchases in the current year were randomly selected and 80 of those were made by singles. In the second study, again 200 house purchases were randomly selected from 5 years ago and 57 of those were made by single people. Test the newspaper's claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper's claim? Let singles now be Population 1 and let singles 5 years ago be Population 2. Step 1. State the null and alternative hypotheses for the test. Fill in the blank below. A) Step 2. Compute the value of the test statistic. Round your answer to two decimal places. Step 3. Draw a conclusion and interpret the decision. A) We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level…2. In a study of jury behavior, two samples of participants were provided details about a trial in which the defendant was obviously guilty. Although group 2 received the san details as group 1, the second group was also told that some evidence had been withheld from the jury by the judge. Later, the participants were asked to recommend a jail sentence. The length of term suggested by each participant is presented here. Is there a significant difference between the two groups in their responses? For Group 1: M = 3, SS = 16, n= 8 For Group 2: M = 6, SS = 24, n = 10 %3D a. Formulate the hypotheses. b. Determine the critical value(s). c. Calculate the test statistic.9. In order to investigate a rumor that there is a greater than expected number of girls among the children of chemists, Science magazine conducted an informal survey of eight chemistry departments. A secretary in the chemistry department at Indiana University, Bloomington, thought there might be something to this rumor and made sure that every one of the 34 faculty members in her department who have children responded to the Science survey. Altogether these Indiana chemists have 53 (56%) girls and 41 (44%) boys. Is this evidence that chemists produce more girl babies than expected? What kind of data would you prefer before drawing this type of conclusion? Explain how your idea would make the evidence produced more convincing.
- 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.7. A new drug study was conducted by a drug company. In the study, 10 people were chosen at random to take Vitamin X for 3 months and then have their cholesterol levels checked. In addition, 10 different people were randomly chosen to take Vitamin Y for 3 months and then have their cholesterol levels checked. All 20 people had cholesterol levels between 8 and 10 before taking one of the vitamins. The drug company wanted to see which of the 2 vitamins had the greatest impact on lowering people's cholesterol. The following data was collected: Vitamin X 7.27.5 5.2 6.5 7.7 10 6.47.6 7.77.8 Vitamin Y 4.8 4.44.5 5.1 6.5 8.03.1 4.6 5.2 6.1 (a) Draw a box-and-whisker plot for both sets of data on the same number line. (b) Use the double box-and-whisker plots to compare the 2 vitamins and provide a conclusion for the drug company. (e) State the skewness of both distributions and justify your answer.16) Tartar is a combination of plaque and minerals from saliva that harden on the surface of teeth. A dentist plans to conduct a study to investigate the following claim made by a toothpaste manufacturer. Toothpaste L is less effective at preventing tartar buildup on teeth than Toothpaste M. The dentist will randomly assign 200 volunteers to use one of two toothpastes, with 100 assigned to use Toothpaste L each day and the remaining 100 assigned to use Toothpaste M each day. Before the study begins, each person will receive a teeth cleaning to remove any tartar buildup. After one month, the dentist will measure the tartar buildup of each person and the number of people who have tartar buildup will be recorded for each toothpaste. The following segmented bar graph shows the results of the study. Toothpaste L 85 15 Tartar buildup O No tartar buildup Toothpaste M 68 32 0.2 0.4 0.6 0.8 1.0 Relative Frequency a) For the 200 volunteers in the study, is there support for the manufacturer's…