I need the 3 attached worksheets completed please.
Ch 21 Practice/Homework Name _____________ Math 207: Intro to Stats Practice Chapter 21 1. In the example from your notes about the college students living at home: a. the 317 is the __________value for the number of students in the sample who were living at home (expected or observes) b. The SD of the box is _______0.41 (exactly equal to or estimated from the data) c. The SE for the number of students in the sample who were living at home is ________ (exactly equal to or estimated from the data as) 2. A simple random sample of size 400 was taken from the population of all manufacturing establishments in a certain state; 11 establishments in the sample had 100 employees or more. Estimate the percentage of manufacturing establishments with 100 employees or more. Attach a standard error to the estimate. 3. Suppose there is a box of 100,000 tickets each marked as 0 or 1. Suppose that in fact, 20% of the tickets in the box are 1’s. Calculate the standard error for the percentage of 1’s in 400 draws from the box. 4. Three different people take simple random samples of size 400 from the box in problem #3 without knowing its contents. The number of 1’s in the first sample is 72, in the second , it is 84 and in the third it is 98. Each person estimates the SE by the bootstrap method. a. The first person estimates the percentage of 1’s in the box as _______and figures this estimate is likely to be off by ______or so. b. The second person estimates the percentage of 1’s in the box as _______and figures this estimate is likely to be off by ______or so. c. The third person estimates the percentage of 1’s in the box as _______and figures this estimate is likely to be off by ______or so. 5. Refer to # 3 and 4 data, Compute a 95% confidence interval for the percentage of 1’s in the box, using the data obtained by the person in exercise 4A. Repeat for the other 2 people. Which of the three intervals cover the population percentage, that is, the percentage of 1’s in the box? Which do not? Remember they do not know the contents of the box but you do. 6. Probabilities are used when reasoning from the _______to the ________; confidence levels are used when reasoning from the ________to the _____________ 7. The chance error is in the ________value. The confidence interval is for the _______percentage. 8. A box contains a large number of red and blue marbles; the proportions of red marbles is known to be 50%. A simple random sample of 100 marbles is drawn from the box. Say whether each of the following statements is true or false and explain why. a. The percentage of red marbles in the sample has an expected value of 50%, and an SE of 5%. b. The 5% measures the likely size of the chance error in the 50%. c. The percentage of reds in the sample will be around 50% give or take 5% of so. d. An approximate 95% confidence interval for the percentage of reds in the sample is 40% to 60%. e. There is about a 95% chance that the percentage of reds in the sample will be in the range from 40% to 60%. CH 20 Practice/Homework Name ___________ Math 207 Intro to Stats Practice Chapter 20 1. A town has 30,000 registered voters, of whom 12,000 are Democrats. A survey organization is about to take a simple random sample of 1000 registered voters. A box model is used to work out the expected value and the SE for the percentage of Deomocrats in the sample. Match each phrase on list A with a phrase or a number on list B (items on list B may be used more than once, or not at all) List A List B population Number of 1’s among the draws Population percentage Percentage of 1/s among the draws sample 40% Sample size box Sample number draws Sample percentage 1000 Denominator for sample percentage 12,000 2. A coin will be tossed 10,000 times. Match the SE with the formula. (one formula will be left over) SE for the….. Formula Percentage of heads 10000 × 50% Number of heads 50 10000 × 100% 10000 × 0. 5 3. The box [0 0 0 1 2] has an average of 0.6 and the SD of 0.8. True or False: The SE for the percentage of 1’s in 400 draws can be found as follows: Justify your answers. SE for number of 1’s = 400 × 0. 8 = 16 SE for percent of 1’s = 16400 × 100% = 4% 4. You are drawing at random from a large box of red and blue marbles. Fill in the blanks: a. The expected value for the percentage of reds in the ____________ equals the percentage of reds in the _______________. b. As the number of draws goes up, the SE for the _____________of reds in the sample goes up but the SE for the _____________of reds goes down. 5. According to the Census, a certain town has a population of 100,000 people ages 18 and over. Of them, 60% are married, 10% have incomes over $75,000 a year, and 20% have college degrees. As part of a pre-election survey, a simple random sample of 1600 people will be drawn from this population. a. To find the chance that 58% or less of the people in the sample are married, a box model is needed. Should the number of tickets in the box be 1600, or 100,000? Explain. Then find the chance. b. To find the chance that 11% or more of the people in the sample have incomes over $75,000 a year, a box model is needed. Should each ticket in the box show the person’s income? Explain. Then find the chance. c. Find the chance that between 19% and 21% of the people in the sample have a college degree. 6. You have hired a polling organization to take a simple random sample from a box of 100,000 tickets, and estimate the percentage of 1’s in the box. Unknown to them the box contains 50% 0’s and 50% 1’s. How far off should you expect them to be: a. If they draw 2500 tickets? b. If they draw 25,000 tickets? c. If they draw 100,000 tickets? Practice/Homework for Chapter 19 Name _________________ Math 207 Intro to Stats Practice/Homework Ch 19 Answer the following questions based off the class discussion on Chapter 19: 1. A survey is carried out at a university to estimate the percentage of undergraduates living at home during the current term. a. a) What is the population? b. b) What is the parameter? 2. The registrar keeps an alphabetical list of all undergraduates, with their current addresses. Suppose there are 10,000 undergraduates in the current term. Someone proposes to choose a number at random from 1 to 100, count that far down the list, taking that name and every 100th name after it for the sample. a. Is this a probability method? Justify your answer b. Is it the same as simple random sampling? Justify your answer. c. Is there selection bias in this method of drawing a sample? Justify your answer. 3. In the Netherlands, all men take a military pre-induction exam at age 18. The exam includes an intelligence test known as “Raven’s progressive matrices” and includes questions about demographic variables like family size. A study was done in 1968, relating the test scores of 18-year old men to the number of their brothers and sisters. The records of all the exams taken in 1968 were used. a. What is the population? b. What is the sample? c. Is there any sampling error? Justify your answer. 4. Polls often conduct pre-election surveys by telephone (land/cell). a. Could this bias the results? Justify your answer b. What if the sample is drawn from the telephone book or random generated google list? 5. Determine if the following are (a) probability methods (b) if they are clusters, simple random , quota or just convenience sampling methods and (c) is there any selection bias a. A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process. b. An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition the Fall semester. Those 100 students are the sample. c. The freshman, sophomore, junior, and senior years are number one, two, three and four, respectively. A random number generator is used to pick two of those years. All students in those two years are in the sample. d. Undergraduate students are organized by certain categories (ex: race, sex, major, etc.). The survey required 3 members from each of the categories to be interviewed by the school newspaper. The newspaper writers determine who they will survey to collect their data.