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Small Business: Bankruptcy The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.
(a) If no preliminary sample is taken to estimate p. how large a sample is necessary to be
(b) In a preliminary random sample of 38 small businesses, it was found that six had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be
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Chapter 8 Solutions
Understanding Basic Statistics
- Color blindness, or dyschromatopsia, is a form of genetic deficiency in color perception. The condition is much more prevalent among males than females, pointing to a genetic connection with the X chromosome. The frequency of dyschromatopsia in the Caucasian American male population is about 7%. However, it is thought that this proportion might be smaller among males of other ethnicities. We want to estimate the proportion of Asian American males who are color-blind. How large a sample size do we need in order to obtain a 95% confidence interval with a margin of error no greater than 5%, or 0.05? Use 0.5 for p̂.arrow_forwardEvery 5 years a city conducts a survey of residents to collect data on various political, economic, an health indicators. With a new survey coming this year the mayor is especially concerned with jobs and the economy. In the last survey only 41% of people in the city said they felt very secure in their job. The mayor wants to be able to estimate that proportion for this year to within a margin of error of +/- 2%. How large of a sample will be needed.arrow_forwardColor blindness, or dyschromatopsia, is a form of genetic deficiency in color perception. The condition is much more prevalent among males than females, pointing to a genetic connection with the X chromosome. The frequency of dyschromatopsia in the Caucasian American male population is about 8%. However, it is thought that this proportion might be smaller among males of other ethnicities. We want to estimate the proportion of Asian American males who are color-blind. How large a sample size do we need in order to obtain a 95% confidence interval with a margin of error no greater than 4%, or 0.04? n=__________arrow_forward
- In a study, a CSULB professor wants to estimate the average grade point averages (GPA) of all students at CSULB. 15 students were randomly surveyed for his study. The GPA of the selected college students are 2.3, 3.3, 2.6, 1.8, 0.2, 3.1, 4.0, 0.7, 2.3, 2.0, 3.1, 3.4, 1.3, 2.6, 2.6. After calculation, the sample mean is 2.35 and the sample standard deviation is 1.03. Assume the population distribution is approximately normal. What is a 90% confidence interval for the population mean?arrow_forwardrowing team consists of three rowers who weigh 42, 36 and 29 pounds. Find all possible random samples with replacement of size three and compute the sample mean for each one. Use them to find the sampling distribution of the sample mean. Also verify the results.arrow_forwardThe state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 1 of 2: Suppose a sample of 333 tenth graders is drawn. Of the students sampled, 260 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places. Step 2 of 2: Suppose a sample of 333 tenth graders is drawn. Of the students sampled, 260 read above the eighth grade level. Using the data, construct the 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.arrow_forward
- During the second semester of SY 2019 – 2020, students in Mathematics in the Modern World were asked to rate their extent of preparation and level of difficulty. Five classes were considered for this study. Suppose 15 students from each class were randomly selected, (4) is there a significant relationship between their level of difficulty and prelim scores? (5) is there a significant relationship between their level of difficulty and midterm scores? (6) is there a significant relationship between the extent of preparation and level of difficulty in their prelim scores?arrow_forwardIUS 2020 reached a sample of 2,401 Internet users and 384 non-Internet users at the national level and a total of 384 Internet users for each state to meet the requirement for state-level surveys. Table 1 shown a percentage of Malaysian internet users for the years 2018 and 2020. Respondents were selected randomly, and the interviews were carried out through telephone interview. IUS 2020 also focuses on emerging Internet issues introduced in the previous surveys; namely online content, online child safety and online privacy/security. From the Table 1, you need to: i. Proposed an analysis on Measures of Central Tendency by using formulae for both years, ii. Justify answer (i) by using graphs for both years, iii. Proposed a suitable chart to show a comparison data for both years, iv. Proposed an analysis on Measures of Dispersion by using formulae for both years,arrow_forwarda) The University of the East Europe is interested in the overall performance of its studentsin the academic year 2020/2021. There were 1460 students registered for this academicyear. The University decides to select a sample of 150 students from each of the 5faculties- Science, Medicine, Law, Social Science and Humanities in proportion to thenumber of students in each faculty. i. Identify the population of interest for this scenario. ii. Identify the sampling technique used by the researcher. iii. State one advantage and one disadvantage of the sampling technique described in thegiven scenario. iv. If the medical faculty has 584 students registered, calculate how many medicalstudents would be part of the sample of 150. b) The Table below shows the average score of the150 students sampled from theUniversity of the East Europe in the academic year 2020/2021. Score (out of 100) Number of students40-49 1950-59…arrow_forward
- _________ error is the difference between a sample statistic and a population parameter that occurs due to chance. Sampling Standard Statistical Humanarrow_forwardno handwriting,please The University of the East Europe is interested in the overall performance of its studentsin the academic year 2020/2021. There were 1460 students registered for this academicyear. The University decides to select a sample of 150 students from each of the 5faculties- Science, Medicine, Law, Social Science and Humanities in proportion to thenumber of students in each faculty.i. Identify the population of interest for this scenario. ii. Identify the sampling technique used by the researcher. iii. State one advantage and one disadvantage of the sampling technique described in thegiven scenario.arrow_forwardDuring the recovery from the Great Recession of 2007-2009, the economic situation for many familiesimproved. However, in 2011 the recovery was slow and it was uncertain as to how much had reallychanged on the national level. To estimate the national average of the percent of low-income workingfamilies, a representative simple random sample of the percent of low-income working families from eachof the country’s reporting jurisdictions could be used to calculate a point estimate and create a relatedconfidence interval. With this confidence interval a better picture of the nation’s recovery can be had andlegislative decisions can be made.6. Describe in two or three sentences how a simple random sample of size n=20 could be obtainedfrom the full list of jurisdictions provided for use with this assignment.7. A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a samplestandard deviation of 6.56%. Use this information to calculate a 90% confidence interval…arrow_forward
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