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Energy Statistics A Guide To Information Sources 1st Edition Sarojini Balachandran - Solutions
4. MegaStat steps to find the confidence interval for the tire tread example are as follows:a. Select MegaStat, Confidence Intervals/Sample Size, and click the Confidence interval - mean tab.b. Enter .81 for the Mean, .23 for the Std. Dev. and 10 for n.c. Select t.d. Select 95% as the Confidence
3. The Excel function to find the t-value is T.INV.2T. For the tire tread example, we would enter “=T.INV.2T(5%,9)” into a cell. The 5% is from 100% - 95% = 5%. The number of degrees of freedom is 10 - 1 = 9.
2. MegaStat steps to find the confidence interval for the store manager’s example are as follows:a. Select MegaStat, Confidence Intervals/Sample Size, and click the Confidence interval - mean tab.b. Enter 55420 for the Mean, 2150 for the Std. Dev. and 256 for n.c. Select z.d. Select 95% as the
1. The Excel function to find the z-value is NORM.S.INV. To find the z-value for a 95% confidence level, we would enter “=NORM.S.INV(97.5%)” into a cell. Note that the function is cumulative, and so 97.5% includes the 95% confidence level plus the area in the lower tail (5%/2 = 2.5%).
3. The City Transport Authority wants to estimate the proportion of central city workers that use public transportation to get to work. A sample of 100 workers revealed 64 used public transportation. Develop a 95% confidence interval.
2. A recent federal report indicated 27% of children ages 2 to 5 ate vegetables at least five times a week. How large a sample is necessary to estimate the true population proportion within 2% with a 98% level of confidence?
1. A recent study of 26 Cobden, Ontario, residents revealed they had lived at their current address for a mean of 9.3 years with a sample standard deviation of 2 years.a. What is the population mean?b. What is the best estimate of the population mean?c. What is the standard error of the mean?d.
10. To locate the appropriate t value, which is not necessary? (degrees of freedom, level of confidence, population mean)
9. The has no effect on the size of the sample. (level of confidence, margin of error, size of the population, variability in the population)
8. The finite population correction factor is used when the sample is more than % of the population. (5, 20, 50, 100)
7. To develop a confidence interval for a proportion, the four conditions of the must be met.
6. To construct a confidence interval for a mean, the z distribution is used only when the population is known.
5. For a 95% confidence interval, approximately percent of the similarly constructed intervals will include the population parameter being estimated.
4. A shows the fraction of a sample that has a particular characteristic.
3. Assuming the same sample size and the same standard deviation, a 90% confidence interval will be than a 95% confidence interval. (equal to, wider, narrower, cannot tell)
2. A is a range of values within which the population parameter is likely to occur
1. A is a single value computed from sample information used to estimate a population parameter.
84. Refer to the real estate data for the Saskatoon area, on Connect, which include information on home listings. Consider this a population, and take a sample of 20 listings.a. Develop a 90% confidence interval for the mean list price of the homes. Does the true population mean fall in the
83. Refer to the CREA data, on Connect, which include information on average house prices nationally and in a selection of cities across Canada. Note: Select only the cities.a. Develop an 80% confidence interval for the mean list price for January 2011.b. Is it possible that the population mean is
82. Refer to the CREA (Canadian Real Estate Association) data, on Connect, which include information on average house prices nationally and in a selection of cities across Canada. Note: Select only the cities.a. Develop a 97% confidence interval for the mean list price for January 2014.b. Is it
81. Refer to the real estate data for the Halifax area, on Connect, which include information on home listings. Consider this a population, and take a sample of 40 listings.a. Develop a 95% confidence interval for the mean list price of the homes. Does the true population mean fall in the
80. The proportion of public accountants who have changed companies within the last three years is to be estimated within 3%. The 95% level of confidence is to be used. A study conducted several years ago revealed that the percentage of public accountants changing companies within three years was
79. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10 979. The standard deviation of the sample was $1000.a. On
78. During a provincial debate on changes to health care, a cable news service performs an opinion poll of 500 small-business owners. It shows that 65% of small-business owners do not approve of the changes. Develop a 95% confidence interval for the proportion opposing health care changes. Comment
77. As a condition of acceptance into a Business Program, the local college requires that applicants must pass a mathematics basic skills test. Of the last 220 applicants, 14 failed the test. Develop a 99% confidence interval for the proportion of applicants that fail the test. Would it be
76. Fashion Industries randomly tests its employees throughout the year. Last year, in the 400 random tests conducted, 14 employees failed the test. Develop a 99% confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that less than 5% of the
75. A film alliance used a random sample of 50 U.S. citizens to estimate that the typical American spent 78 hours watching videos and DVDs last year. The standard deviation of this sample was 9 hours.a. Develop a 95% confidence interval for the population mean number of hours spent watching videos
74. A random sample of 25 people who purchased tickets to the Limelight Theatre on a regular basis stated they paid an average of $65.00 per ticket. The sample standard deviation was $6.25 per ticket.a. What is the population mean? What is the best estimate of the population mean?b. Develop a 99%
73. The National Collegiate Athletic Association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season was 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard
72. Marty Rowatti recently assumed the position of director of the YMCA. He would like some current data on how long current members of the YMCA have been members. To investigate, suppose he selects a random sample of 40 current members. The mean length of membership of those included in the sample
71. As part of their business promotional package, the Costa Rica Chamber of Commerce would like an estimate of the mean cost per day to lease a one-bedroom apartment. A random sample of 40 apartments currently available for lease showed the mean cost per day was $323. The standard deviation of
70. Passenger comfort is influenced by the amount of pressurization in an airline cabin. Higher pressurization allows a closer-to-normal environment and a more relaxed flight. A study by an airline user group recorded the corresponding air pressure on 30 randomly chosen flights. The study revealed
69. A survey of 36 randomly selected “iPhone” owners showed that the purchase price has a mean of $416 with a sample standard deviation of $180.a. Compute the standard error of the sample mean.b. Compute the 95% confidence interval for the mean.c. How large a sample is needed to estimate the
68. The Manitoba Tourism Board plans to sample information centre visitors entering the province to learn the fraction of visitors who plan to camp in the province. Current estimates are that 35% of visitors are campers. How large a sample would you take to estimate at a 95% confidence level the
67. A sample of 352 subscribers to Wired magazine shows the mean time spent using the Internet is 13.4 hours per week, with a sample standard deviation of 6.8 hours. Find the 95% confidence interval for the mean time Wired subscribers spend on the Internet.
66. As part of an annual review of its accounts, a discount brokerage selects a random sample of 36 customers. Their accounts are reviewed for total account valuation, which showed a mean of $32 000, with a sample standard deviation of $8200. What is a 90% confidence interval for the mean account
64. The National Bank, like most other large banks, found that using automatic teller machines (ATMs) reduces the cost of routine bank transactions. National installed an ATM in the corporate offices of the Fun Toy Company. The ATM is for the exclusive use of Fun’s 605 employees. After several
63. An employment agency wants to update an estimate of the proportion of accountants who have changed companies within the last three years, to be estimated within 3%. A 95% level of confidence is to be used. A study conducted several years ago revealed that the percentage of accountants
62. You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence level and state that the estimated proportion must be within 2% of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How
61. You are to conduct a sample survey to determine the mean family income in a rural area. The question is, how many families should be sampled? In a pilot sample of 10 families, the standard deviation of the sample was $500. The sponsor of the survey wants you to use the 95% confidence level. The
60. You need to estimate the mean number of travel days per year for outside salespeople. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If you must estimate the population mean within 2 days, how many outside salespeople should you sample? Use the 90%
59. It is claimed that 60% of households now subscribe to cable TV. You would like to verify this statement for your class in mass communications. If you want your estimate to be within 5 percentage points, with a 95% level of confidence, how large of a sample is required?
58. The bank in Cobden, Ontario, has 650 chequing account customers. A recent sample of 50 of these customers showed 26 to have a Visa card with the bank. Construct the 99% confidence interval for the proportion of chequing account customers who have a Visa card with the bank.
57. Brampton’s traffic patrol reports 500 traffic citations were issued last month. A sample of 35 of these citations showed the mean amount of the fine was $54, with a standard deviation of $4.50. Construct a 95% confidence interval for the mean amount of a citation in Brampton.
56. In a poll to estimate the prime minister’s popularity, each person in a random sample of 1000 voters was asked to agree with one of the following statements: 1. The prime minister is doing a good job. 2. The prime minister is doing a poor job. 3. I have no opinion. A total of 560 respondents
55. There are 20 000 eligible voters in York County. A random sample of 500 York County voters revealed 350 plan to vote to re-elect their current member of parliament. Construct a 99% confidence interval for the proportion of voters in the county who plan to re-elect the returning member. From
54. Furniture Land surveyed 600 consumers and found that 414 were enthusiastic about a new home dècor it plans to show in its store in High Point. Construct the 99% confidence interval for the population proportion.
53. Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the
52. The manufacturer of a new line of ink jet printers would like to include as part of its advertising the number of pages a user can expect from a print cartridge. A sample of 10 cartridges revealed the following number of pages printed: 2698 2028 2474 2395 2372 2475 1927 3006 2334 2379a. What is
51. The Simcoe County Food Emporium claims that “the typical customer spends $60 per visit.” A sample of 12 customers revealed the following purchases, in dollars, spent last visit: $64 66 64 66 59 62 67 61 64 58 54 66a. What is the point estimate of the population mean?b. Develop a 90%
50. An important factor in selling a residential property is the number of people who look through the home. A sample of 15 homes recently sold in the Halifax, Nova Scotia, area revealed the mean number looking through each home was 24 and the standard deviation of the sample was 5 people. Develop
49. A study of 25 graduates of colleges revealed the mean amount owed by a student was $14 381. The standard deviation of the sample was $1892. Construct a 90% confidence interval for the population mean. Is it reasonable to conclude that the mean of the population is actually $15 000? Explain why
48. A recent study by an automobile dealer revealed the mean amount of profit per car sold for a sample of 20 salespeople was $290, with a standard deviation of $125. Develop a 95% confidence interval for the population mean.
47. A student conducted a study and reported that the 95% confidence interval for the mean ranged from 46 to 54. He was sure that the mean of the sample was 50, that the standard deviation of the sample was 16, and that the sample was at least 30 but could not remember the exact number. Can you
46. The employees of Electronics Inc. would like to have a dental plan as part of their benefits package. The question is: how much does a typical employee and his or her family spend per year on dental expenses? A sample of 45 employees reveals the mean amount spent last year was $1820, with a
45. The manager of Apache Burger felt that an average of 70 customers made purchases daily between the hours of 3 p.m. and 5 p.m. A random sample over 50 days showed the sample mean to be 68.6 customers with a standard deviation of 8.2 hours.a. Using the sample data, construct a 99% confidence
44. A restaurant group collected information on the number of meals eaten outside the home per week by young married couples who lived in large cities. A survey of 60 couples showed the sample mean number of meals eaten outside the home was 2.76 meals per week, with a standard deviation of 0.75
43. The Badik Construction Company limits its business to constructing decks. The mean time to construct one of its standard decks is 8 hours for a two-person construction crew. The information is based on a sample of 40 decks recently constructed. The standard deviation of the sample was 3
42. A recent survey of 50 executives who were laid off from their previous position revealed it took an average of 26 weeks for them to find another position. The standard deviation of the sample was 6.2 weeks. Construct a 95% confidence interval for the population mean. Is it reasonable that the
41. A recent study of 50 self-service gasoline stations in a metropolitan area revealed that the mean price of unleaded gas was $1.30 per litre. The sample standard deviation was $0.07 per litre.a. Determine a 99% confidence interval for the population mean price.b. Would it be reasonable to
40. A meat inspector has been given the assignment of estimating the mean net mass of packages of ground chuck labelled “1.4 kg.” Of course, he realizes that the masses cannot be precisely 1.4 kg. A sample of 36 packages reveals the mean mass to be 1.401 kg, with a standard deviation of 0.01
39. A random sample of 85 group leaders, supervisors, and similar personnel at General Motors revealed that, on the average, they spent 6.5 years on the job before being promoted. The standard deviation of the sample was 1.7 years. Construct a 95% confidence interval.
38. Past surveys reveal that 30% of tourists going to Las Vegas to gamble during a weekend spend more than $1000. Management wants to update this percentage.a. The new study is to use the 90% confidence level. The estimate is to be within 1% of the population proportion. What is the necessary
37. Suppose that the prime minister wants an estimate of the proportion of the population that supports his current policy on health care. The prime minister wants the estimate to be within 0.04 of the true proportion. Assume a 95% level of confidence. The prime minister’s political advisors
36. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the mass of the boxes, a few were checked. The mean mass was 9.3 kg, the standard deviation 0.23 kg. How many boxes must the
35. A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. It is desired to estimate the mean viewing time within one-quarter hour. The 95% level
34. The estimate of the population proportion is to be within plus or minus 0.10, with a 99% level of confidence. The best estimate of the population proportion is 0.45. How large a sample is required?
33. The estimate of the population proportion is to be within plus or minus 0.05, with a 95% level of confidence. The best estimate of the population proportion is 0.15. How large a sample is required?
32. We want to estimate the population mean within 5, with a 99% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required?
31. A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 95% level of confidence. How large a sample is required?
30. There are 300 welders employed at the Weller Shipyards Corporation. A sample of 30 welders revealed that 18 had graduated from a registered welding course. Construct the 95% confidence interval for the proportion of all welders who graduated from a registered welding course.
29. A shipment of 500 dolls is received by Panda Importers. The quality control manager selects a random sample of 75 to test. Five are found to be defective. Construct a 90% confidence interval for the population proportion of defective dolls in the shipment. Would it be reasonable to find 10
28. Sixty items are randomly selected from a population of 900. The number of defective items is found to be 12. Develop a 95% confidence interval for the population proportion of defective items.
27. The attendance at the Foresters Falls baseball game last night was 400. A random sample of 50 of those in attendance revealed that the mean number of soft drinks consumed per person was 1.86, with a standard deviation of 0.50. Develop a 99% confidence interval for the mean number of soft drinks
26. Forty-nine items are randomly selected from a population of 500 items. The sample mean is 40, and the sample standard deviation 9. Develop a 99% confidence interval for the population mean.
25. Thirty-six items are randomly selected from a population of 300 items. The sample mean is 35, and the sample standard deviation 5. Develop a 95% confidence interval for the population mean.
24. Schadek Silkscreen Printing Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He
23. The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and
22. Ms. Maria Wilson is considering running for mayor of her town. Before completing her nomination papers, she decides to conduct a survey of voters. A sample of 400 voters reveals that 300 would support her in the November election.a. Estimate the value of the population proportion.b. Compute the
21. The owner of the West End Kwick Fill Gas Station wished to determine the proportion of customers who use his pay-at-the-pump feature. This feature allows customers to use a credit card at the pump and never enter the station. He surveyed 100 customers and found that 80 paid at the pump.a.
20. Seventy-three percent of the 500 students surveyed voted in favour of the new breakfast menu in the college cafeteria.a. Estimate the value of the population proportion of those college students who would prefer the new menu.b. Compute the standard error of the proportion.c. Determine a 95%
19. Out of a sample of 200 students, 75 indicated that they preferred chocolate ice cream to vanilla ice cream.a. Estimate the value of the population proportion of those who preferred chocolate ice cream.b. Compute the standard error of the proportion.c. Determine a 90% confidence interval for the
18. An automobile insurance company wants to estimate the mean time workers who are employed in the downtown office spend getting to work. A sample of 15 workers reveals the following number of minutes travelled: 29 38 38 33 38 21 45 34 40 37 37 42 30 29 35 Develop a 98% confidence interval for the
17. Taylor Industries and Caldwell Securities are considering jointly offering child care for their employees. As a part of the feasibility study, they wish to estimate the mean weekly child care cost of their employees. A sample of 10 employees who use child care reveals the following amounts, in
16. The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 27 kilograms (kg) with a standard deviation of 9 kg. Assume a normal population.a. What is the value of the population mean? What is the best
15. The owner of Britten’s Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month.a. What is the value of the population mean? What is the best estimate of this
14. A sample of 25 observations is selected from a normal population where the sample standard deviation is 4.75. The sample mean is 16.85.a. Determine the standard error of the mean.b. Determine the 98% confidence interval for the population mean.c. If you wanted a narrower interval, would you
13. A sample of 20 observations is selected from a normal population. The sample standard deviation is 26.25, and the sample mean is 75.a. Determine the standard error of the mean.b. Determine the 90% confidence interval for the population mean.c. If you wanted a wider interval, would you increase
12. Use Appendix B.2, Excel, or another software package to locate the value of t under the following conditions:a. The sample size is 15, and the level of confidence is 95%.b. The sample size is 24, and the level of confidence is 98%.c. The sample size is 12, and the level of confidence is 90%.
11. Use Appendix B.2, Excel, or another software package to locate the value of t under the following conditions:a. The sample size is 12, and the level of confidence is 95%.b. The sample size is 20, and the level of confidence is 90%.c. The sample size is 8, and the level of confidence is 99%.
10. Dr. Patton is a professor of English. Recently, she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal distribution with a standard deviation of 2.44 words per essay. For her Tuesday class of 40
9. Bob Nale is the owner of Nale’s Texaco Gas Town. Bob would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume that the number of litres sold follows the normal distribution with a standard deviation of 10 L. From his records, he selects a random sample of
8. Refer to the previous exercise. Suppose that 64 smokers (instead of 49) were sampled. Assume that the sample mean remained the same.a. What is the 95% confidence interval estimate of μ?b. Explain why this confidence interval is narrower than the one determined in the previous exercise.
7. A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal distribution with a standard deviation of $5. A sample of 49 steady smokers revealed that X = 20.a. What is
6. Suppose that you know σ and you want an 85% confidence level. What value would you use to multiply the standard error of the mean?
5. A sample of 25 observations is selected from a normal population where the population standard deviation is 4.75. The sample mean is 16.85.a. Determine the standard error of the mean.b. Determine the 98% confidence interval for the population mean.c. If you wanted a narrower interval, would you
4. A sample of 40 observations is selected from a normal population where the population standard deviation is 25. The sample mean is 75.a. Determine the standard error of the mean.b. Determine the 90% confidence interval for the population mean.c. If you wanted a wider interval, would you increase
3. A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 5. The sample mean is 20.a. Determine the standard error of the mean.b. Explain why we can use formula (8–1) to determine the 95% confidence interval, even though the
2. A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean.
1. A sample of 49 observations is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99% confidence interval for the population mean.
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