Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1. A new teacher is analyzing whether or not there is an association between scores earned by students on their first exam in the course and the course grade earned by students at the end of the term. Exams are scored using a 100 point scale (0 to 100 points) and course grades use a 100% scale (0% to 100%). There are 35 students in the course. HaL Find the equation of the regression line y` = a + b x. The mean and standard deviation for the Course Grade variable is 0.766 and 0.123 The mean and standard deviation for the Exam 1 Score variable is 83.943 and 11.295 The correlation is 0.7845 Be very sensitive to roundoff errors. HbL Predict the course grade for a student who scores a 91 on their first exam. Use the equation of the regression line found in (b). 2. A Gallup Poll asked "Do you think the United States needs to: change its current strategy in Iraq, keep its current strategy, but change its tactics, or keep both its current strategy and tactics in Iraq? ... Nearly 6 in 10 Americans (59%) say the United States should change its strategy in Iraq." Gallup's report said "Results for this panel study are based on telephone interviews with 1,001 national adults, aged 18 and older, conducted Oct. 23-26, 2006." Furthermore, the article included the statements "For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls." HaL HbL Describe in as much detail as possible given the excerpts from the article above the population. How many members of the sample felt that the United States should change its strategy in Iraq? HcL If the confidence level was changed from 95% to 99% would the maximum margin of sampling error be (1) less than 3%, (2) greater than 3%, or (3) remain at 3%? HdL Suppose that there are 240 million adults living in the US. How many members of the population described by the article would you estimate feel that the United States should change its strategy in Iraq? 3. Choose an adult aged 25 years or over at random. The probability is 0.151 that the person chosen did not complete high school, 0.322 that the person has a high school diploma but no further education, and 0.289 that the person has at least a bachelor's degree. HaL What must be the probability that a randomly chosen adult has some education beyond high school but does not have a bachelor's degree? HbL 4. What is the probability that a randomly chosen young adult has at least a high school education? The distribution of the weights of all bags of M&M candies measured in grams is NH48.5, 1.3L: 44.6 45.9 47.2 48.5 49.8 51.1 52.4 HaL If a single bag of M&M's was selected at random, what is the probability that the weight of the bag would be between 48 grams and 48.5 grams? HbL If a SRS of 40 bags of M&M's was selected and the average weight of the 40 bags was computed, what is the probability that the average weight for the 40 bags would be between 48 grams and 48.5 grams? Suppose a population is composed of uniformly distributed values ranging from 0 to 90 ( m = 45 and 5. s = 25.98 ). The population distribution is shown below. Uniformly Distributed Population 0 20 40 60 80 HaL What is the probability that a single value selected from the population would be greater than 40 and less than 45? HbL What is the probability that a SRS of size 100 taken from this population would have a sample mean greater than 40 and less than 45? To estimate the mean height m of adult women in your city, you will measure an SRS of adult women. 6. You know from government data that heights of adult women are approximately Normal with standard deviation 2.3 inches. How large an SRS do you need to collect so that the standard deviation of êê x is 0.25? 7. To estimate the mean weight of all bags of M&M candies you collect a SRS of 75 bags and find the average weight of the 100 bags to be 48.95 grams. Give a 96% confidence interval for the mean weight of all bags of M&M's. Assume s = 1.4 for the weights of all bags of M&M's. 8. You would be satisfied to estimate the mean weight of all bags of M&M's to within ± 0.1 grams with 95% confidence. How many bags of M&M candies must be in your SRS? Assume s = 1.4 for the weights of all bags of M&M's. 9. The mean height of American women is about 64 inches, with standard deviation about 2.7 inches. The mean height of American men is about 69 inches, with standard deviation about 2.8 inches. If the correlation between the heights of husbands and wives is about r = 0.5, find the equation of the regression line that will predict the height of the wife when given the height of the husband. 10. Use your answer from the previous problem to predict the height of the wife of a man who is 72 inches tall. Would you consider this estimate to be an accurate one? 11. A study of children in elementary school shows a high positive correlation between the heights and scores on a test of reading comprehension. Johnny, an exceptionally bright and tall fifth grader concludes that he must have a high reading comprehension. Explain to Johnny what is wrong with his conclusion. 12. The following is a list of the 10 most popular boys names. Susy wants to name her newborn son one of these names, but can't decide which one to use. Use line 108 of table B to find a SRS of size 3 of the names in the list, so that Susy will only have three names to chose from. AIDAN ETHAN CADEN JADEN CALEB DYLAN JACOB CONNOR LOGAN HAYDEN 13. A political scientist wants to know how college students feel about the Social Security program. The scientist obtains a list of all the students at WWCC and mails a questionnaire to 200 of the students selected at random. Based upon 98 returned surveys the scientist concludes that college students are dissatisfied with the Social Security program. What are the population and sample of this study? 13. A political scientist wants to know how college students feel about the Social Security program. The scientist obtains a list of all the students at WWCC and mails a questionnaire to 200 of the students selected at random. Based upon 98 returned surveys the scientist concludes that college students are dissatisfied with the Social Security program. What are the population and sample of this study? 14. Give an explanation for what is wrong with the conclusion of the study described in the previous problem. 15. Read the description for each of the following studies, then answer the question. Study 1: A publishing company wants to measure the effectiveness of one of its textbooks. The company tests a group of students for comprehension and then divides the students into two groups. One group uses the book and one doesn't. The company then retests the students and compares the results. Study 2: A political scientist wants to know how college students feel about the Social Security program. The scientist obtains a list of all the students at WWCC and mails a questionnaire to 200 of the students selected at random. Based upon 98 returned surveys the scientist concludes that college students are dissatisfied with the Social Security program. For each study, determine whether it is an observational study or an experiment and give reasons for your answers. 16. In a bag full of marbles there are three red marbles, five blue marbles, and seven yellow marbles. Give the probability model for the act of drawing one marble at random from the bag (i.e. what is the sample space and probability of each event). 17. What is the probability of drawing either a red marble or a blue marble? Explain your answer using the appropriate probability rule. 18. Voter registration records in a small town in Washington show that 52% of all voters are Republican. On Mayberry Ave., 50 people are polled and it is found that 49% of them are Republican. Which of these numbers is a parameter and which is a statistic? Explain your answers. 19. The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65g and standard deviation 5g. Think of cartons of such eggs as SRSs of size 12 from the population of all eggs. What is the approximate distribution of the mean weight from each carton of eggs? 20. For the situation described in the previous problem, what is the probability that the weight of a carton falls between 750g and 825g? 21. A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 200 students was 135 minutes. Suppose we know that the study time of all first year students at this university follows a Normal distribution with standard deviation s = 60 minutes. Find a 99% confidence interval for the mean study time of all first-year students. 22. How large a sample is needed to cut the margin of error for the previous problem to 6? 23. If the distribution of the study time of all first year students at this university didn't follow a Normal distribution but still had standard deviation s = 60, could you still find the same confidence interval asked for above? Give a reason for your answer. 24. A manufacturer of small appliances wants to estimate retail sales of its hand mixers by gathering information from a sample of retail stores. This month an SRS of 75 stores finds that these stores sold an average of 24 mixers, with standard deviation 11. Give a 95% confidence interval for the mean number of mixers sold by all stores.