Math 110 Fall 2013 Name ______________________ Final Exam Remember: Write down the formula from the outline if used! 1. The paper “I Smoke But I am not a Smoker” (Journal of American College Health [2010]) describes a survey of 899 college students who were asked about their smoking behavior. Of the students surveyed, 268 classified themselves as nonsmokers, but said yes when asked later in the survey if they smoked. These students were classified as “phantom smokers”, meaning that they did not view themselves as smokers even though they do smoke at times. The authors were interested in using these data to determine if there is convincing evidence that more than 25% of college students fall into the phantom smoker category. Test the author’s claim at a 5% significance level. 1 2. Thirty percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection. a) Among 15 randomly selected cars, what is the probability that 5 fail the inspection? b) Among 15 randomly selected cars, find the mean and the standard deviation of the number of cars that fail the inspection. c) Would it be unusual to find that 10 of the 15 cars would fail the inspection? Why or why not? 3. The Internet is affecting us al in many different ways, so there are many reasons for estimating the proportion of adults who use it. Assume that the manager of EBay wants to determine the current percentage of U. S. adults who now use the Internet. How many people must be surveyed in order to be 95% confident that the sample percentage is within 3 percentage points? 2 4. Many people believe that criminals who pear guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample data for San Francisco defendants in burglary cases. All of the subjects had prior prison sentences. Guilty Plea Not Guilty Plea Sent to Prison 392 58 Not Sent to Prison 564 14 If one person is randomly selected, find each of the following. a) Find the probability that the person pled guilty. b) Find the probability that the person was sent to prison. c) Find the probability that the person pled guilty and was sent to prison. d) Find the probability that the person pled guilty or was sent to prison. e) Find the probability that the person pled guilty given that the person was sent to prison. f) Find the probability that the person was sent to prison given that the person pled guilty. g) Are the events “pleading guilty” and “being sent to prison” mutually excusivie events? Why or why not? h) Was the data collected qualitative or quantitative? 3 i) Use a 5% significance level to test the claim that the sentence (being sent to prison or not) is independent of the plea. j) If you were an attorney defending a guilty defendant would these results suggest that you should encourage a guilty plea? k) Construct a 95% confidence interval for the proportion of defendants who plead guilty and went to prison. 4 5. A company sent seven of its employees to attend a course in building selfconfidence. These employees were evaluated for their self-confidence before and after attending this course. The following table gives the scores (on a scale of 1 to 15, 1 being the lowest and 15 being the highest) of these employees before and after they attended the course. Before After 8 10 5 8 4 5 9 11 6 6 9 7 5 9 Test at the 1% significance level whether attending this course increases the mean score of employees. 5 6. In a 1993 survey of 560 college students, 171 said that they used illegal drugs during the previous year. In a recent survey of 720 college student, 263 said that they used illegal drugs during the previous year. Use a 5% significance level to test the claim that the proportion of college students using illegal drugs in 1993 was less than it is now. 6 7. Assume that heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. a) A day bed is 72 inches long. What is the probability that a randomly selected man’s height will exceed the length of the day bed? b) In designing a new bed, you want the height of the bed to equal or exceed the height of at least 95% of all men. What is the minimum length of the bed? 8. Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches. 235 159 492 530 138 125 128 900 360 212 a) Is the data collected qualitative or quantitative? b) Find the mean, median, standard deviation and variance for the above data. c) Are there any unusual data above? Why or why not? d) Which average would you use for this data? Why or why not? e) Would you describe the data above as discrete or continuous? Why? 7 f) Construct a 95% confidence for the population mean salaries. 9. Identify the level of measurement as nominal, ordinal, discrete or continuous. a) The eye colors of all fellow students in your statistics class b) The pulse rates of students in your statistics class as they are taking this exam c) A movie’ critics rating of “must see, recommended, not recommended, don’t even think about going” d) The actual temperatures in degrees Fahrenheit of the rooms in this building during final exams e) The number on the back of a football uniform f) The number of students who pass their final exams today 10. Seventy-two percent of Americans squeeze their toothpaste from the top. This and other not-so-serious findings are included in The First Really Important Survey of American Habits. Those results are based on 7000 responses from the 25000 questionnaires that were mailed. a) Is the 72% a statistic or a parameter? Explain. b) Does the survey constitute an observational study or an experiment? 8 11. For women aged 18 – 24, systolic blood pressure (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension is commonly defined as systolic blood pressure above 140. a) If a woman between the ages of 18 - 24 is randomly selected, find the probability that her systolic blood pressure is greater than 140. b) If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140. c) Given that part (b) involves a sample size that is not larger than 30 why can the Central Limit Theorem be used? d) If a physician is given a report that women have a mean systolic blood pressure below 140, can she conclude that none of the women have hypertension (with blood presser greater than 140)? Explain. 12. Identify which of these types of sampling is used: random, systematic, stratified, cluster or convenience. a) On the day of the last presidential election, ABC News organized an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left the premises. b) The author of a statistics textbook once observed sobriety checkpoints in which every 5th driver was stopped an interviewed. c) A statistics instructor surveyed all of her students to obtain sample data consisting of the number of credit cards that college student possess. 9 d) A student organization wants to assess the attitudes of students toward a proposed change in the hours than the undergraduate library is open. They randomly select 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors. 13. The following table represents sample data collected on the pulse rates of female students. Pulse Rate Frequency 60 - 89 12 70 – 79 14 80 - 89 11 90 - 99 1 100 – 109 1 110 – 119 0 120 – 129 1 a) Find the class width? b) Find the class midpoints. c) Construct a relative frequency table. d) Construct a cumulative frequency table. e) Find the mean and the standard deviation. f) Was the data collected qualitative or quantitative? g) Was the data collected discrete or continuous? 10 14. Researches collected a simple random sample of the times that 81 college students required to earn their bachelor’s degrees. The sample has a mean of 4. 8 years with a standard deviation of 2.2 years. Use a 5% significance level to test the claim that the mean time for all college students to earn a degree is greater than 4.5 years. 11 15. Listed below are the numbers of years that popes and British monarch (since 1690) lived after their election or coronation. Treat the data as simple random samples from a larger population. Popes 9 23 5 21 15 15 3 2 0 6 6 26 10 32 2 18 25 11 11 6 8 25 17 23 19 6 25 13 36 12 15 13 33 59 10 7 63 Monarchs 17 9 a) Are the samples independent or dependent? b) Find the mean and the standard deviation for the number of years lived after election of the popes. c) Find the mean and the standard deviation for the number of years lived after coronation of the monarchs. d) Use a 1% significance level to test the claim that the mean longevity for popes is less than the mean for British monarchs 12 16. Replacement times for CD players are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years (based on data from “Getting Things Fixed,” Consumer Reports). If you want to provide a warranty so that only 1% of the TV sets will be replaced before the warranty expires, what is the time length of the warranty? 17. True False The way that a question in a survey is worded rarely has an effect on the responses. 18. True False Large samples usually give reasonably accurate results, no matter how they are drawn. 19. True False The variance and standard deviation are measures of center. 20. Two variables have a ______________ relationship if the data tend to cluster around a straight line. 21. True False If we reject H0, we conclude that H0 is false. 22. True False If there is no linear relationship between paired date, we use y as the best predicted value. 24. State the assumptions needed to do a hypothesis test about several population means (an ANOVA test). 13 25. The following table lists the salaries of randomly selected individuals from four large metropolitan areas. At the 5% significance level, can you conclude that the mean salary is different in at least one of the areas? Pittsburgh 27,800 28,000 25,500 29,150 30,295 Dallas 30,000 33,900 29,750 25,000 34,055 Chicago 32,000 35,800 28,000 38,900 27,245 Minneapolis 30,000 40,000 35,000 33,000 29,805 Anova: Single Factor SUMMARY Groups Pittsburgh Dallas Chicago Minneapolis Count 5 5 5 5 ANOVA Source of Variation Between Groups Within Groups SS 83622620 238558480 Total 322181100 Sum 140745 152705 161945 167805 df 3 16 Average 28149 30541 32389 33561 Variance 3192130 13813030 24975855 17658605 MS 27874206.67 14909905 F 1.869509341 P-value 0.175443187 19 14 F crit 3.238871

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