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In a company made up of 20,000 employees, 4,000 (20%) are enrolled in an optional savings program. The company is considering changing the program and decides to first take a poll of 400 randomly selected employees. In this problem we will look at the sample percentage of employees who are enrolled in the program.
(a) Consider the box model for this problem. The percentage of 1’s in the box is: known OR estimated (circle one).
(b) Consider the percentage of employees in the sample who are enrolled in the program.
What is its
What is its standard error? __________%
(c) Use the normal approximation to calculate the chance that the percentage of employees in the sample who are enrolled in the program is between 19% and 21%.
Answer: _____________%
(d) How do you justify using the normal approximation in (c)?
(Your answer should include the name of a theorem and one or more numerical comparisons.)
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- For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. 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 The National Council 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 99% sure that a point estimate p will be within a distance of 0.09 from p? (Round your answer up to the nearest whole number.) small businesses (b) In a preliminary random sample of 30 small businesses, it was found that twelve had declared Chapter 11 bankruptcy. How many more small businesses should be included in the sample to be 99% sure that a point estimate p will be within a distance of 0.090 from p? (Round your answer up…A nutritionist estimates that 57% of her patients stick to the eating plan she helps them design. She also knows that 53% of her patients are diabetic. Additionally she knows that 22.79% of her patients are diabetic and are not sticking to the eating plan she helped them design. (a) What proportion of her patients are not sticking to the eating plan she helped them design? (b) What proportion of her patients are diabetic? (c) Within the nutritionist's patients, being diabetic and not sticking to the eating plan she helped design are which of the following? O dependent O independentTo determine the amount of sugar in a typical serving of breakfast cereal, a student randomly selected 60 boxes of different types of cereal from the shelves of a large grocery store. The student noticed that the side panels of some of the cereal boxes showed sugar content based on one-cup servings, while others showed sugar content based on three- quarter-cup servings. Many of the cereal boxes with side panels that showed three-quarter-cup servings were ones that appealed to young children, and the student wondered whether there might be some difference in the sugar content of the cereals that showed different-size servings on their side panels. To investigate the question, the data were separated into two groups. One group consisted of 29 cereals that showed one-cup serving sizes; the other group consisted of 31 cereals that showed three-quarter cup serving sizes. The boxplots shown below display sugar content (in grams) per serving of the cereals for each of the two serving sizes.…
- The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Percent of Books on Subject in CirculationLibrary on This Subject Number of Books inSample on This Subject Business 32% 237 Humanities 25% 220 Natural Science 20% 223 Social Science 15% 128 All other subjects 8% 80 Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance?State the null and alternate hypotheses. H0: The distributions are the same.H1: The distributions are different.H0: The distributions are the same.H1: The distributions are the same. H0: The distributions are different.H1: The distributions are different.H0: The…In a US presidential election, the incumbent president wins with 51.5% of the vote to 48.2% for the primary challenger (and .3% to others). In a nationwide telephone poll of 1000 people conducted exactly one week before the election by a university polling group, 49% of people polled supported the incumbent president, 50% supported the challenger, and 1% supported other candidates. a. For the polling study, what was the population of interest? b. What was the sample? c. Why did the sample results differ from the population? d. What are two constants that might have limited the generalizability of the polling results?Consumer Reports rated automobile insurance companies and gave annual premiums for top-rated companies in several states. The figure below shows premiums for urban customers (married couple with one 17-year-old son) in three states. The box plots were all drawn using the same scale on a TI-8- Texas Pennsylvania California (a) Which state has the lowest premium? the highest? O lowest, California; highest, Texas O lowest, Texas; highest, Pennsylvania O lowest, Pennsylvania; highest, California lowest, California; highest, Pennsylvania
- The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Percent of Books on Subject in CirculationLibrary on This Subject Number of Books inSample on This Subject Business 32% 267 Humanities 25% 217 Natural Science 20% 222 Social Science 15% 109 All other subjects 8% 73 Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance?State the null and alternate hypotheses. H0: The distributions are different.H1: The distributions are the same.H0: The distributions are the same.H1: The distributions are different. H0: The distributions are the same.H1: The distributions are the same.H0: The…At an assembly plant, workers assemble parts for a piece of farm equipment. The supervisor conducted an experiment to compare the effectiveness of three assembly methods, A, B, and C. Eighteen employees were randomly assigned, six employees each, to one of the three methods. After completing their training, each person was asked to assemble five pieces of equipment using his or her training method. The average time to complete the assembly of all five pieces of equipment was recorded. (a) What type of study design is used? O independent groups design O repeated measures design O matched pairs design O randomized block design What are the experimental units in this study? O the 18 employees O the five pieces of equipment to be assembled O the three assembly methods O the average time to assemble five pieces of equipment (b) What are the treatments? O the 18 employees O the five pieces of equipment to be assembled O the three assembly methods the average time to assemble five pieces of…A choral conductor has 1885 singers in her choir, some of them are professional singers. The conductor wants to estimate what percentage of singers are professional, but can't ask all 1885, so she instead asks 630 singers in front and finds 17 who are professionals. (a) Identify the sample.A. 17/1885B. 630C. singers who were askedD. None of the above. (b) Identify the populationA. percentage of entire singers who are professionalB. entire singersC. 17/1885D. None of the above. (c) What specific type of bias does this scenario demonstrate?A. Voluntary response samplingB. Convenience SamplingC. It is representative of the population.D. None of the above. (d) Identify the parameterA. range of values in which 95% values fallB. percentage of entire singers who are professionalC. 17D. None of the above.
- What type of study would you conduct if you wanted to know how many hours a week on average students at your school spend on homework? Explain your reasoning. Problem 2 Select all designs which describe an observational study that is not a survey. A: 200 voters are randomly selected and asked how they will vote in the upcoming election. B: 60 pieces of lumber are randomly selected. Half of those are randomly assigned to be treated with a new sealer. Three months later the level of rotting in all the pieces is recorded. C: 100 pregnant women are randomly selected. For 8 weeks, the level of iron in their blood and their vital signs are recorded. D: 400 incoming sixth grade students are randomly selected. Researchers record their results on a reading test at the beginning and end of the school year and compare the level of improvement seen in students at elementary schools to students at middle schools. E: 300 people apply to test a new mattress. 100 of these customers are…According to a census company. 7 1% of all bables bom are of low birth weight. An obstetrician wanted to know whether mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight babies. She randomly selected 240 births for which the mother was 35 to 39 years old and found 28 low-birth-weight bables. Complete parts (a) through (c) below. (a) lf the proportion of low-birth-welght babies for mothers in this age group is 0.071, compute the expected number of low-birth-weight births to 35- to 39-year-old mothers. What is the expected number of births to mothers 35 to 39 years old that are not low birth weight? The expected number of low birth-weight births to 35- to 39-year-old mothers is The expected number of births to mothers 35 to 39 years old that are not low birth weight is (Type integers o decimals)The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below. Subject Area Business Humanities. Natural Science Social Science All other subjects USE SALT Percent of Books on Subject in Circulation Library on This Subject 32% 25% 20% 15% 8% Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students. (a) What is the level of significance? State the null and alternate hypotheses. Ho: The distributions are different. H₁: The distributions are different. H: The distributions are different. H: The distributions are the same. H₁: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are different.…
