• Whenever you are asked to generate a confidence interval or hypothesis test, do not forget to express your conclusion inwritten form as demonstrated in lectures.• Do not use the bootstrap for any examples unless specifically asked to do so. (Not all assignments require bootstrapping.)• Data Sets: For any problems in which a data set is required, you can download the data set from D2L. Go to the content taband you will see Data Sets at the bottom. Simply clicking on any data set should allow you to download it to your computer.• Deciding on Ha vs Ho: Remember that we (the people doing the research and hypothesis test) typically use the "accepted" or"previous" values as our Ho, and we use our "newer" hypothesis, or the thing we are trying to prove, as Ha. If you havequestions on this assignment as to what should be used as H. vs Ha, I don't mind if you discuss this in the class discussiongroup.• Formatting the H, vs H, statement: Note that H, and Ho are not values! So if for example, we are talking about a mean ageof 34.6, we should never say something like: Ha = 34.6. Instead, we should say things like:o Ho mean age = 34.6o H Mean time to execute the process > 143 millisecondsProblemsProblem #1In a discussion of the average SATM (math SAT) scores of California high school students, an educational expert points out thatbecause only those high school students planning on attending college will take the SAT, there is in fact, a selection bias at work.The person claims that if all California HS students were to take the test, the score would be 450 or even lower. As an experiment,a random sample of 500 students were given the test, and the mean was found to be 461, with a standard deviation of 100. Is ourexpert's claim borne out? Do a complete hypothesis test, demonstrating your understanding of each step. (You don't have toexplain in extreme detail, just demonstrate your understanding of the steps involved). Use the standard value for alpha.

Let us start solving step by step. .. Sample size 50.. Sample mean 461 Sample standard deviation 100…

Answered: Problem #1 In a discussion of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In 2014, Scotland was considering independence from England, going so far as to take a referendum vote. One opinion poll taken at the time showed that 51% of Scots favored "independence." In another poll taken at that same time, only 34% favored being "separate" from England. The primary reason these results differed by so much is that a. samples will usually differ just by chance due to random sampling. b. the wording of questions has a big effect on poll results. c. more follow-up efforts reduced the nonresponse rate of the second poll. d. the sample sizes are different, so the margins of error are different.
This question refers to a survey of a university's faculty members on affirmative action policies for the university. The survey was based on telephone interviews with a random sample of 1,001 faculty members conducted in December 1995. One of the questions asked was, "Do you favor or oppose using race, religion, sex, color, ethnicity, or national origin as a criterion for admission to the university?" Of the 704 male respondents, 45% said "Favor," and of the 297 female respondents, 72% said "Favor." (a) Find the conservative margin of error (in %) for the male respondents. (Round your answer to one decimal place.) % Use the conservative margin of error to compute an approximate 95% confidence interval for the percent who favored this policy at the time of the poll in the population of male faculty members. (Round your answers to one decimal place.) (_,_)% , % (b) Find the conservative margin of error (in %) for the females. (Round your answer to one decimal…
An article about the California lottery gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and 64 years old, and 14% are 65 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article. Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with ? = 0.05. Age of Purchaser Frequency 18–34 36 35–64 130 65 and over 34 Calculate the test statistic. (Round your answer to two decimal places.) ?2 = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? The data strong evidence to conclude…
A research group conducted an extensive survey of 2940 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1470 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. How large a sample is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1.6% of the population percentage? (Hint: Use p ≈ 0.50 as a preliminary estimate. Round your answer up to the nearest whole number.) workers
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?
The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1079 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample size Groups mean variance Less than h.s. High school Bachelor's 258 40.9 101.8 263 41.8 97.5 270 42.2 94.4 Graduate 288 43.0 98.7 Send data to calculator Send data to Excel To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the following statistic. Variation between the samples F= Variation within the samples For the data from…
A research group conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1467 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. How large a sample is needed f we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 2.6% of the population percentage? (Hint: Use p≈ 0.50 as a preliminary estimate. Round your answer up to the nearest whole number.) USE SALT workers
The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled. Use a = 0.05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. Source Sum of Squares Degrees Mean Square F P-value of Variation (to whole number) of Freedom (to 2 decimals) (to 2 decimals) (to 4 decimals) X X (X) * X * * Treatments Error Total The p-value is less than 0.01…
A political scientist claims that 38% of first-year college students characterize themselves as being “moderate” or “middle of the road” as far as their political affiliation is concerned. Believing this claimed value is too high, you survey a random sample of 400 first-year college students and find that 120 characterize themselves as being “moderate” or “middle of the road.” Based on this information, what will the test statistic be? Choose the answer below that is closest to what you calculate, and try not to do a lot of rounding until you get to the very end of your calculations. 1. -0.3 2. -1.2 3. -2.6 4. -3.3 5. None of the other answer options are correct because the test statistic should be positive, not negative.
Sierra College students enrolled in an online Elementary Statistics course were asked to participate in an anonymous onlne survey. The survey asked the students "Which type of device will you primarily use to access your online course in Canvas?". Of the 152 students who answered this question, 20 responded "a desktop computer", 121 responded "a laptop computer", 6 responded "a smartphone", and 5 responded "a tablet". The Sierra College Mathematics Department believes that less than 5% of students enrolled in an online Elementary Statistics course primarily uses a smartphone to access their online course in Canvas. Use the data collected in the survey to conduct a hypothesis testing procedure to test this belief. What conclusion should be reached according to the results of this hypothesis test?
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…
Suppose a community college has 10,000 students (the population). We are interested in the average amount of money a part-time student spends on books in the fall term. Asking all 10,000 students is almost an impossible task. A sample is taken using a list of students who take photography classes, and each of these students is surveyed. Do you think that this sample is representative of the entire 10,000 student population? Why or why not?

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