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statistics principles and methods
Questions and Answers of
Statistics Principles And Methods
=+The sample included suburban Cook County plus DuPage, Kane, Lake, McHenry, and Will Counties. In a sample of this size, one can say with 95% certainty that results will differ by no more than 3
=+9.60 An article in the Chicago Tribune (August 29, 1999)reported that in a poll of residents of the Chicago suburbs, 43% felt that their financial situation had improved during the past year. The
=+The proportion of defective handles p is of interest. How many handles from the shipment should be inspected to estimate p to within 0.1 with 95% confidence?
=+9.59 A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and must be discarded. A large shipment
=+p 5 .77). Construct a 95% confidence interval for p, the true proportion of all households that use coupons.
=+9.58 Retailers report that the use of cents-off coupons is increasing. The Scripps Howard News Service (July 9, 1991) reported the proportion of all households that use coupons as .77. Suppose that
=+Association quoted very different figures regarding the proportion of primary-care physicians who have participated in some form of doctor-assisted suicide for terminally ill patients (USA Today,
=+9.57 The 1991 publication of the book Final Exit, which includes chapters on doctor-assisted suicide, caused a great deal of controversy in the medical community. The Society for the Right to Die
=+random sample from the population of full-time workers, use this information to construct and interpret a 90% confidence interval estimate of p, the true proportion of fulltime workers so angered
=+9.56 An Associated Press article on potential violent behavior reported the results of a survey of 750 workers who were employed full time (San Luis Obispo Tribune, September 7, 1999). Of those
=+d. Based on the interval in Part (a), do you think that the mean number of hours worked per week for nonpersisters is greater than 20? Explain.
=+c. The 98% confidence interval for persisters is narrower than the corresponding interval for nonpersisters, even though the standard deviation for persisters is larger than that for nonpersisters.
=+b. Consider the 257 persisters as a random sample from the population of all persisters at the university where the data were collected. Compute a 98% confidence interval for the mean number of
=+a. Consider the 44 nonpersisters as a random sample from the population of all nonpersisters at the university where the data were collected. Compute a 98% confidence interval for the mean number
=+factors that affect whether students stay in college. The following summary statistics are based on data from a sample of 44 students who did not return to college after the first quarter (the
=+9.55 The article “Selected Characteristics of High-Risk Students and Their Enrollment Persistence” (Journal of College Student Development [1994]: 54–60) examined
=+b. The interval in Part (a) does not include 0. Does this imply that all students lie to their mothers? Explain.
=+a. Suppose that this group of 77 is a random sample from the population of students at this university. Construct a 95% confidence interval for the mean number of lies per conversation for this
=+9.54 Seventy-seven students at the University of Virginia were asked to keep a diary of a conversation with their mothers, recording any lies they told during these conversations (San Luis Obispo
=+interpret a 90% confidence interval for p, the true proportion of Utah residents who favor fluoridation. Is this interval consistent with the statement that fluoridation is favored by a clear
=+9.53 In the article “Fluoridation Brushed Off by Utah”(Associated Press, August 24, 1998), it was reported that a small but vocal minority in Utah has been successful in keeping fluoride out of
=+What sample size would you recommend for this study?
=+a preliminary estimate of p and then using the conservative value of .5. How do the two sample sizes compare?
=+survey to estimate this proportion for the adult residents of your city. What is the required sample size if you want to estimate this proportion to within .05 with 95% confidence? Compute the
=+9.52 The article “Consumers Show Increased Liking for Diesel Autos” (USA Today, January 29, 2003) reported that 27% of U.S. consumers would opt for a diesel car if it ran as cleanly and
=+all citizens should be tested. Use this information to estimate p, the true proportion of all U.S. adults who favor AIDS testing of all citizens.
=+9.51 Despite protests from civil libertarians and gay rights activists, many people favor mandatory AIDS testing of certain at-risk groups, and some people even believe that all citizens should be
=+ Can you find a combination for which it has a capture rate that is even farther from 95% than it was for n 5 40 and p 5 .3? How does the modified interval perform in each of these cases?
=+3. Experiment with different combinations of values of sample size and population proportion p. Can you find a combination for which the large sample z interval has a capture rate that is close to
=+2. How does the proportion of intervals constructed that include p 5 .3, the population proportion, compare to 95%? Is this proportion closer to 95% than was the case for the large-sample z
=+a. How does the proportion of intervals constructed that contain m 5 100 compare to the stated confidence level of 95%? On how many intervals was your proportion based? (Note—if you followed the
=+What would be the appropriate formula for determining sample size when the desired confidence level is 90%?98%?
=+9.50 The formula described in this section for determining sample size corresponds to a confidence level of 95%.
=+0.1 oz with 95% confidence? Assume that s is known to be 1 oz.
=+and that no one ever throws away a copy of National Geographic. A key to the analysis presented in the article is the weight of an issue of the magazine. Suppose that you were assigned the task of
=+9.49 ▼ The article “National Geographic, the Doomsday Machine,” which appeared in the March 1976 issue of the Journal of Irreproducible Results (yes, there really is a journal by that
=+9.48 The Bureau of Alcohol, Tobacco, and Firearms(BATF) has been concerned about lead levels in California wines. In a previous testing of wine specimens, lead levels ranging from 50 to 700 parts
=+a confidence interval for m, the true mean calories per half-cup serving of chocolate ice cream? Explain why or why not.
=+9.47 ● ▼ The following data are the calories per half-cup serving for 16 popular chocolate ice cream brands reviewed by Consumer Reports (July 1999):270 150 170 140 160 160 160 290 190 190 160
=+b. Suppose that you wanted to make a statement about the range of GPAs for students at this university. Is it reasonable to say that 95% of the students at the university have GPAs in the interval
=+a. Construct a 95% confidence interval for the mean high school GPA for students at this university.
=+9.46 The article “First Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students” (Journal of College Student Development
=+Assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months
=+9.45 ● Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked how many months had passed since their last visit to a
=+9.44 ● Fat contents (in percentage) for 10 randomly selected hot dogs were given in the article “Sensory and Mechanical Assessment of the Quality of Frankfurters”(Journal of Texture Studies
=+9.42 The authors of the paper “Short-Term Health and Economic Benefits of Smoking Cessation: Low Birth Weight” (Pediatrics [1999]: 1312–1320) investigated the medical cost associated with
=+c. Based on your interval in Part (a), if flight 448 is scheduled to depart at 10 A M., what would you recommend for the published arrival time? Explain.
=+b. Give an interpretation of the 90% confidence level associated with the interval estimate in Part (a).
=+a. Compute and interpret a 90% confidence interval for the mean airborne time for flight 448.
=+9.41 ● ▼ Example 9.3 gave the following airborne times for United Airlines flight 448 from Albuquerque to Denver on 10 randomly selected days:57 54 55 51 56 48 52 51 59 59
=+mer and 195 lb for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).
=+a. Construct and interpret a 95% confidence interval for the m Fronb. C the m Fronc. T
=+to estimate average passenger plus carry-on weights.They found an average summer weight of 183 lb and a winter average of 190 lb. Suppose that each of these estimates was based on a random sample
=+9.39 Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old
=+d. If appropriate, construct and interpret a 99% confidence interval for the mean anticipated Halloween expense for Canadian residents.
=+vc. Is it appropriate to use the t confidence interval to estimate the mean anticipated Halloween expense for Canadian residents? Explain why or why not.
=+b. Is it reasonable to think that the distribution of the variable anticipated Halloween expense is approximately normal? Explain why or why not.
=+a. Explain how it could be possible for the standard deviation of the anticipated Halloween expense to be larger than the mean anticipated expense.
=+a survey of 1000 randomly selected Canadian residents.Each individual in the sample was asked how much he or she anticipated spending on Halloween during 2005. The resulting sample mean and
=+9.38 The article “Most Canadians Plan to Buy Treats, Many Will Buy Pumpkins, Decorations and/or Costumes”(Ipsos-Reid, October 24, 2005) summarized results from
=+minutes and 24.2 minutes, respectively. Construct and interpret a 90% confidence interval for the mean commute time of working adult Calgary residents.
=+9.37 Five hundred randomly selected working adults living in Calgary, Canada were asked how long, in minutes, their typical daily commute was (Calgary Herald Traffic Study, Ipsos, September 17,
=+c. The interval (.768, 1.302) is either a 90% confidence interval or a 99% confidence interval for the mean TV viewing time for children less than 12 months old. Is the confidence level for this
=+b. Now suppose that the sample standard deviations for the three age group samples were equal, but that the three sample sizes might have been different. Which of the three age group samples had
=+a. Suppose that the sample sizes for each of the three age group samples were equal. Based on the given confidence intervals, which of the age group samples had the greatest variability in TV
=+average TV viewing time (in hours per day) for three different age groups.Age Group 95% Confidence Interval Less than 12 months (0.8, 1.0)12 to 23 months (1.4, 1.8)24 to 35 months (2.1, 2.5)
=+9.36 The article “The Association Between Television Viewing and Irregular Sleep Schedules Among Children Less Than 3 Years of Age” (Pediatrics [2005]: 851–856)reported the accompanying 95%
=+306.09 Newtons and 41.97 Newtons, respectively. Assuming that it is reasonable to assume that breaking force under these conditions has a distribution that is approximately normal, estimate the
=+9.35 ▼ Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six
=+c. Consider the following statement: If the process of selecting a sample of size 50 and then computing the corresponding 95% confidence interval is repeated 100 times, 95 of the resulting
=+b. Consider the following statement: There is a 95%chance that m is between 7.8 and 9.4. Is this statement correct? Why or why not?
=+a. Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer.
=+9.34 Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined. Let m denote the average alcohol content
=+9.33 ▼ Samples of two different types of automobiles were selected, and the actual speed for each car was determined when the speedometer registered 50 mph. The resulting 95% confidence intervals
=+b. The confidence level for one of these intervals is 90%and for the other it is 99%. Which is which, and how can you tell?
=+a. What is the value of the sample mean resonance frequency?
=+9.32 The two intervals (114.4, 115.6) and (114.1, 115.9)are confidence intervals for m 5 true average resonance frequency (in hertz) for all tennis rackets of a certain type.
=+d. 90% confidence, n 5 25e. 90% confidence, n 5 13f. 95% confidence, n 5 10
=+9.31 The formula used to compute a confidence interval for the mean of a normal population when n is small is What is the appropriate t critical value for each of the following confidence levels
=+e. 24 df, outside the interval from 22.80 to 2.80f. 24 df, to the right of 2.80 g. 10 df, to the left of 21.81
=+9.30 Given a variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region?a. 10 df, between 21.81 and 1.81b. 10
=+store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within.05 with 95% confidence?
=+9.29 ▼ A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular
=+9.27 The Gallup Organization conducts an annual survey on crime. It was reported that 25% of all households experienced some sort of crime during the past year. This estimate was based on a
=+9.26 USA Today (October 14, 2002) reported that 36% of adult drivers admit that they often or sometimes talk on a cell phone when driving. This estimate was based on data from a sample of 1004
=+b. What assumptions are necessary for the confidence interval in Part (a) to be valid?c. To what population would it be reasonable to generalize the confidence interval estimate from Part (a)?
=+a. Construct a 90% confidence interval for the proportion who can identify their own country on a blank world map.
=+9.24 The National Geographic Society conducted a study that included 3000 respondents, age 18 to 24, in nine different countries (San Luis Obispo Tribune, November 21, 2002). The society found
=+c. Give two reasons why the confidence interval in Part (a)is wider than the confidence interval in Part (b).
=+b. Construct and interpret a 90% confidence interval for the proportion of U.S. medical residents who have a credit card debt of more than $3000.
=+a. Construct and interpret a 95% confidence interval for the proportion of U.S. medical residents who work moonlighting jobs.
=+115 residents, 38 reported that they worked moonlighting jobs and 22 reported a credit card debt of more than $3000.Suppose that it is reasonable to consider this sample of 115 as a random sample
=+9.23 The article “Doctors Cite Burnout in Mistakes” (San Luis Obispo Tribune, March 5, 2002) reported that many doctors who are completing their residency have financial struggles that could
=+c. Based on the confidence intervals from Parts (a) and(b), comment on the apparent inconsistency in the responses given by the individuals in this sample.
=+b. Construct a 90% confidence interval for the proportion of adult American who think that it is often or sometimes OK to lie to avoid hurting someone’s feelings.
=+a. Construct a 90% confidence interval for the proportion of adult Americans who think lying is never justified.
=+52% responded that lying was never justified. When asked about lying to avoid hurting someone’s feelings, 650 responded that this was often or sometimes OK.
=+9.22 One thousand randomly selected adult Americans participated in a survey conducted by the Associated Press(June, 2006). When asked “Do you think it is sometimes justified to lie or do you
=+9.21 The article “Viewers Speak Out Against Reality TV”(Associated Press, September 12, 2005) included the following statement: “Few people believe there’s much reality in reality TV: a
=+(b) are not the same width even though they both have a confidence level of 95%.
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