\fJoong Won Mo Assignment Homework4 due 07/01/2016 at 11:59pm PDT (incorrect) 1. (1 pt) An experiment investigated the effect of length and repetition of TV ads on students choosing to eat at Del Taco. All 60 students watched a 40-minute television program that included ads for Del Taco. Some students saw a 30-second commerical; others a 90-second commerical. The same commerical was shown either 1, 3, or 5 times during the program. After the viewing, each student was asked to rate their craving for Del Taco on a scale of 0 to 10. What are the subjects of this experiment? A. effect of length and repetion of TV ads B. 40-minute television program C. 1, 3, or 5 commercials during the 40-minute television program D. 60 students E. craving for Del Taco on a scale of 0 to 10 5. (1 pt) Canada has two official languages, English and French. Choose a Canadian at random and ask, \"What is your mother tongue?\" Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region: Language English Probability 0.63 French Asian/Pacific 0.22 0.06 Other ? (a) What probability should replace \"?\" in the distribution? (b) What is the probability that a Canadian's mother tongue is not English? (c) What is the probability that a Canadian's mother tongue is a language other than English or French? (a) (b) (c) Answer(s) submitted: Answer(s) submitted: (incorrect) 2. (1 pt) For the Del Taco experiment, what are the factors? A. 60 students B. craving for Del Taco on a scale of 0 to 10 C. 40-minute television program D. 1, 3, or 5 commercials during the 40-minute television program E. length and repetition of TV ads (incorrect) 6. (1 pt) Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2007. Color Probability Answer(s) submitted: White Silver 0.19 0.18 Black 0.16 Red 0.13 Gray Blue 0.12 0.12 (a) What is the probability that the vehicle you choose has any color other than the six listed? (b) What is the probability that a randomly chosen vehicle is neither Silver nor Gray? (a) (b) (incorrect) 3. (1 pt) (a) In the Del Taco experiment, how many treatments are there? answer: Answer(s) submitted: Answer(s) submitted: (incorrect) 4. (1 pt) For the Del Taco experiment, what is the response variable? A. 60 students B. craving for Del Taco on a scale of 0 to 10 C. 30-second and 90-second commericials D. 1, 3, or 5 commercials during the 40-minute television program E. 40-minute television program (incorrect) 7. (1 pt) A couple plans to have three children. There are 8 possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally likely. (a) Write down all 8 arrangements of the sexes of three children in a list separated by commas. (b) What is the probability of any one of these arrangements above? (c) Let X be the number of girls the couple has. What is the Answer(s) submitted: Math243Summer-Evitts 1 probability that X = 3? (b) (c) (a) (incorrect) 11. (1 pt) A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y. (a) Write the event \"the student could run a mile in more than 6.73 minutes\" in terms of the value of the random variable Y. Use the symbols \"\" or \"\" as appropriate to indicate the bounds on Y. Answer(s) submitted: (incorrect) 8. (1 pt) Canada's national statistics agency, Statistics Canada, says that the land area of Canada is 9,094,000 square kilometers. Of this land, 4,176,000 square kilometers are forested. Choose a square kilometer of land in Canada at random. (a) What is the probability that the area you choose is forested? (b) What is the probability that it is not forested? (a) (b) (b) What is the probability of the event from part (a)? Answer(s) submitted: (incorrect) Answer(s) submitted: 12. (1 pt) Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is s = 8 milligrams. Juan repeats the measurement 5 times and records the mean x of his 5 measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 5 measurements and averaging them, what would be the standard deviation of all his x0 s?) (incorrect) 9. (1 pt) Let Y be a random number between 0 and 1 produced by the uniform distribution as discussed in idealized random number generator described in Figures 10.4 and 10.5 and Example 10.8 of the 6th edition of Moore, Notz and Fligner. Find the following probabilities: (a) P(Y 0.1) (b) P(Y < 0.1) (c) P(0.1 Y 0.3) (a) (b) (c) (b) How many times must Juan repeat the measurement to reduce the standard deviation of x to 2? (a) (b) Answer(s) submitted: Answer(s) submitted: (incorrect) 13. (1 pt) Sheila's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with = 120 mg/dl and s = 10 mg/dl. (a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes? (incorrect) 10. (1 pt) Generate two random numbers between 0 and 1 and take X to be their sum. The sum X can take any value between 0 and 2. The density curve of X is the triangle shown in Figure 10.7 (p. 275) of the 6th edition of Moore, Notz and Fligner. (a) What is the probability that X is less than 1.3? (b) What is the probability that X is less than 0.9? (a) (b) Answer(s) submitted: 2 (b) If measurements are made on 7 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes? (a) (b) (incorrect) 17. (1 pt) Andrew plans to retire in 34 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. (a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 34 years will exceed 10%? (b) What is the probability that the mean return will be less than 7%? (a) (b) Answer(s) submitted: (incorrect) 14. (1 pt) Sheila's measured glucose level one hour after a sugary drink varies according to the Normal distribution with = 120 mg/dl and s = 15 mg/dl. What is the level L such that there is probability only 0.1 that the mean glucose level of 4 test results falls above L ? L= Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 18. (1 pt) Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 15. (1 pt) The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7. (a) What are the mean and standard deviation of the average number of moths x in 60 traps? 114 108 111 104 89 120 132 74 112 102 91 111 128 107 103 114 118 98 114 103 119 86 96 112 105 72 112 93 These 31 girls are an SRS of all seventh-grade girls in the school district. Suppose that the standard deviation of IQ scores in this population is known to be s = 15. We expect the distribution of IQ scores to be close to Normal. Estimate the mean IQ score for all seventh-grade girls in the school district, using a 95% confidence interval. to (b) Use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.7. (a) mean: standard deviation: (b) Answer(s) submitted: Answer(s) submitted: (incorrect) 19. (1 pt) It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 4 minutes. A random sample of 75 oil changes yielded a sample mean of 29 minutes. Compute the 95% confidence interval estimate for the population mean. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. Confidence Interval = (incorrect) 16. (1 pt) An insurance company knows that in the entire population of millions of homeowners, the mean annual loss from fire is = $300 and the standard deviation of the loss is s = $900. The distribution of losses is strongly right skewed: most policies have $0 loss, but a few have large losses. If the company sells 10,000 policies, what is the probability that it can safely base its rates on the assumption that its average loss will be no greater than $305? Answer(s) submitted: Answer(s) submitted: 100 130 103 (incorrect) 3 20. (1 pt) Example 14.1 (page 352) described NHANES survey data on the body mass index (BMI) of 654 young women. The mean BMI in the sample was x = 26.8. We treated these data as an SRS from a Normally distributed population with standard deviation s = 7.5. (a) Give three confidence intervals for the mean BMI in this population, using 90%, 95%, and 99% confidence. (b) What are the margins of error for 90%, 95%, and 99% confidence? How does increasing the confidence level change the margin of error of a confidence interval when the sample size and population standard deviation remain the same? to (1) 90%: 95%: to 99%: to (2) 90%: 95%: 99%: (incorrect) 22. (1 pt) The data below represent a random sample of 9 scores on a statistics quiz. (The maximum possible score on the quiz is 10.) Assume that the scores are normally distributed with a standard deviation of 2.4. Estimate the population mean with 92% confidence. 6 10 6 5 4 7 4 9 8 Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. Confidence Interval = Answer(s) submitted: (incorrect) 23. (1 pt) The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 10 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds with confidence level 96%. Sample Size = Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 21. (1 pt) A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 17 minutes. How large a sample should she take to make an estimate within 4 minutes of the mean time with 98% confidence? Sample Size = 24. (1 pt) A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight loss is about 12 pounds. How large a sample should he take to estimate the mean weight loss to within 5 pounds, with 92% confidence? Sample Size = Answer(s) submitted: Answer(s) submitted: (incorrect) Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 4 Joong Won Mo Assignment Homework5 due 07/01/2016 at 11:59pm PDT Math243Summer-Evitts (incorrect) 1. (1 pt) 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 252 students was x = 134 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation = 65 minutes in the population of all first-year students at this university. Use the survey result to give a 99% confidence interval for the mean study time of all first-year students. to 4. (1 pt) The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitude toward school. Scores range from 0 to 200. The mean score for college students is about 115, and the standard deviation is about 30. A teacher suspects that the mean for older students is higher than 115. She gives the SSHA to an SRS of 9 students who are at least 30 years old. Suppose we know that scores in the population of older students are Normally distributed with standard deviation = 30. We seek evidence against the claim that = 115. What is the sampling distribution of the mean score x of a sample of 9 students if the older students don't differ from typical college students? sample mean: sample standard deviation: Answer(s) submitted: (incorrect) Answer(s) submitted: 2. (1 pt) Emissions of sulfur dioxide by industry sett off chemical changes in the atmosphere that result in \"acid rain\". The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviation = 0.5. A sample of n days finds that the mean pH is x = 4.8. Give a 95% confidence interval for the mean pH for each sample size n = 5, n = 15, n = 40. The intervals give a picture of what mean pH values are plausible for each sample. n = 5: to n = 15: to n = 40: to (incorrect) 5. (1 pt) The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitude toward school. Scores range from 0 to 200. The mean score for college students is about 115, and the standard deviation is about 30. A teacher suspects that the mean for older students is higher than 115. She gives the SSHA to an SRS of students who are at least 30 years old. Suppose we know that scores in the population of older students are Normally distributed with standard deviation = 30. State the null and alternative hypotheses for the study of older students' attitudes. Note: Type in \"mu\" as the substitute for and \"!=\" for 6=. H0 : Ha : Answer(s) submitted: Answer(s) submitted: (incorrect) 6. (1 pt) The average height of 18-year-old American women is 64.2 inches. You wonder whether the mean height of this year's female graduates from your local high school is different from the national average. You measure an SRS of 78 female graduates and find that x = 63.1 inches. What are your null and alternative hypotheses? Note: Type in \"mu\" as the substitute for and \"!=\" for 6=. H0 : Ha : (incorrect) 3. (1 pt) Example 14.1 assumed that the body mass index (BMI) of all American young women follows a Normal distribution with standard deviation = 7.5. How large a sample would be needed to estimate the mean BMI in this population to within 1.8 with 95% confidence? n= Answer(s) submitted: Answer(s) submitted: 1 two numbers does the P - value lie? (e) Does the test give good evidence against the null hypothesis? (Answer with \"Yes/Y\" or \"No/N\".) (a) (b) (c) (d) z: between and P -value: between and (e) (incorrect) 7. (1 pt) A test of H0 : = 1 against Ha : > 1 has test statistic z = 1.59. Answer \"Yes/Y\" or \"No/N\" to the following questions. Is this test significant at the 2% level ( = 0.02)? Is it significant at the 0.5% level ( = 0.005)? Answer(s) submitted: Answer(s) submitted: (incorrect) 8. (1 pt) A test of H0 : = 1 against Ha : 6= 1 has test statistic z = 1.8. Answer \"Yes/Y\" or \"No/N\" to the following questions. Is this test significant at the 5% level ( = 0.05)? Is it significant at the 2% level ( = 0.02)? (incorrect) Answer(s) submitted: 10. (1 pt) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 240 yards on average. Suppose a random sample of 164 golfers be chosen so that their mean driving distance is 236.2 yards. The population standard deviation is 42.9. Calculate the followings for a hypothesis test where H0 : = 240 and Ha : < 240 : (incorrect) 9. (1 pt) A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1. If this is true, the numbers generated come from a population with = 0.5 and = 0.2887. A command to generate 121 random numbers gives outcomes with mean x = 0.4364. Assume that the population remains fixed. We want to test H0 : = 0.5 Ha : 6= 0.5 (a) Calculate the value of the z test statistic. (b) Use Table C: is z significant at the 40% level ( = 0.4)? (Answer with \"Yes/Y\" or \"No/N\".) (c) Use Table C: is z significant at the 0.1% level ( = 0.001)? (Answer with \"Yes/Y\" or \"No/N\".) (d) Between which two Normal critical values z in the bottom row of Table C does the absolute value of z lie? Between what (a) test statistic (b) p-value p = Answer(s) submitted: (incorrect) c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 2