MS1023 Business Statistics with Computer Applications MS1023 Business Statistics w/Comp Apps I Homework #3 - Use Red Par Score Form Chp. 7: Questions 1-50 1. Kristen Ashford purchased the subscribers list for Wind Surfing magazine. She plans to survey a sample of the subscribers before using the list in her mail order business. She chooses the first 100 of the 5,000 names. Her sample is a _________. a) simple random sample b) stratified sample c) systematic sample d) convenience sample e) cluster sample 2. Kristen Ashford purchased the subscribers list for Wind Surfing magazine. She plans to survey a sample of the subscribers before using the list in her mail order business. She randomly selects the fourth name as a starting point and then selects every 50th subsequent name (54, 104, 154, etc.). Her sample is a _________. a) simple random sample b) stratified sample c) systematic sample d) convenience sample e) cluster sample 3. Kristen Ashford purchased the subscribers list for Wind Surfing magazine. She plans to survey a sample of the subscribers before using the list in her mail order business. The names are numbered consecutively from 1 to 5,000. Kristen chooses her sample by selecting four-digit numbers (1 to 5,000) from a random number table. Her sample is a _________. Homework #3 b) stratified sample c) systematic sample d) convenience sample e) cluster sample 4. A carload of palletized aluminum castings has arrived at Mansfield Motor Manufacturers. The car contains 1,000 pallets of 100 castings each. Mario Munoz, manager of Quality Assurance, directs the receiving crew to deliver the 127th and 869th pallets to his crew for 100% inspection. Mario randomly selected 127 and 869 from a table of random numbers. Mario's sample of 200 castings is a _____________. a) simple random sample b) systematic sample c) stratified sample d) cluster sample e) convenience sample 5. Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10 workers from each of the six departments. Abel's sample is a ________________. a) proportionate systematic sample b) proportionate stratified sample c) disproportionate systematic sample d) disproportionate stratified sample e) proportionate cluster sample a) simple random sample Maho Sonmez maho.sonmez@utsa.edu 1 MS1023 Business Statistics with Computer Applications 6. Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10% of the workers from each of the six departments. Abel's sample is a ________________. a) proportionate systematic sample b) proportionate stratified sample c) disproportionate systematic sample d) disproportionate stratified sample e) proportionate cluster sample Homework #3 9. According to the central limit theorem, if a sample of size 100 is drawn from a population with a mean of 80, the mean of all sample means would equal _______. a) 0.80 b) 8 c) 80 d) 100 e) 120 10. According to the central limit theorem, if a sample of size 64 is drawn from a population with a mean of 56, the mean of all sample means would equal _______. a) 7.00 b) 56.00 c) 64.00 d) 0.875 e) 128.00 7. Catherine Chao, Director of Marketing Research, needs a sample of households to participate in the testing of a new toothpaste package. She chooses thirty-six of her closest friends. Catherine's sample is a _____________. 11. According to the central limit theorem, if a sample of size 100 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal _______. a) cluster sample b) convenience sample c) quota sample d) systematic sample e) random sample a) 0.80 b) 8 c) 80 d) 800 e) 0.080 8. Catherine Chao, Director of Marketing Research, needs a sample of households to participate in the testing of a new toothpaste package. She directs the seven members of her staff to find five households each. Catherine's sample is a _____________. a) cluster sample b) proportionate stratified sample c) quota sample d) disproportionate stratified sample e) simple random sample 12. According to the central limit theorem, if a sample of size 64 is drawn from a population with a standard deviation of 80, the standard deviation of sample means would equal _______. Maho Sonmez maho.sonmez@utsa.edu a) 10.000 b) 1.250 c) 0.125 d) 0.800 e) 0.080 2 MS1023 Business Statistics with Computer Applications 13. Increasing the sample size causes the sampling distribution of x to ________. a) shift to the right b) shift to the left c) have more dispersion d) have less dispersion e) stay unchanged 14. According to the central limit theorem, for samples of size 64 drawn from a population with = 800 and = 56, the mean of the sampling distribution of sample means would equal _______. a) 7 b) 8 c) 100 d) 800 e) 80 15. According to the central limit theorem, for samples of size 64 drawn from a population with = 800 and = 56, the standard deviation of the sampling distribution of sample means would equal _______. a) 7 b) 8 c) 100 d) 800 e) 80 16. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of more than 95 is _______. a) 0.1056 b) 0.3944 Maho Sonmez maho.sonmez@utsa.edu Homework #3 c) 0.4286 d) 0.8944 e) 1.0000 17. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of less than 84 is _______. a) 0.9332 b) 0.0668 c) 0.4332 d) 0.8664 e) 1.0000 18. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean between 85 and 95 is _______. a) 0.1056 b) 0.3944 c) 0.7888 d) 0.2112 e) 0.5000 19. Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean between 80 and 100 is _______. a) 0.9876 b) 0.0124 c) 0.4938 d) 0.0062 e) 1.0000 3 MS1023 Business Statistics with Computer Applications 20. Suppose a population has a mean of 450 and a variance of 900. If a random sample of size 100 is drawn from the population, the probability that the sample mean is between 448 and 453 is _______. a) 0.4972 b) 0.6826 c) 0.4101 d) 0.5899 e) 0.9878 21. Suppose a population has a mean of 870 and a variance of 1,600. If a random sample of size 64 is drawn from the population, the probability that the sample mean is between 860 and 875 is _______. a) 0.9544 b) 0.6826 c) 0.8785 d) 0.5899 e) 0.8185 22. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 14 minutes is ________. a) 0.4772 b) 0.0228 c) 0.9772 d) 0.9544 e) 1.0000 23. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating Maho Sonmez maho.sonmez@utsa.edu Homework #3 the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 16 minutes is ________. a) 0.4772 b) 0.0228 c) 0.9072 d) 0.9544 e) 0.9772 24. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean less than 15 minutes is ________. a) 0.5000 b) 0.0228 c) 0.9072 d) 0.9544 e) 1.0000 25. Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers. Accordingly, he plans a sample of waiting times for walk-in customers. If the population of waiting times has a mean of 15 minutes and a standard deviation of 4 minutes, the probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is ________. 4 MS1023 Business Statistics with Computer Applications a) 0.9974 b) 0.4987 c) 0.9772 d) 0.4772 e) 0.5000 26. Suppose 40% of the population possess a given characteristic. If a random sample of size 300 is drawn from the population, then the probability that 44% or fewer of the samples possess the characteristic is _______. a) 0.0793 b) 0.4207 c) 0.9207 d) 0.9900 e) 1.0000 27. Suppose 30% of a population possess a given characteristic. If a random sample of size 1200 is drawn from the population, then the probability that less than 348 possess that characteristic is _______. a) 0.2236 b) 0.2764 c) 0.2900 d) 0.7764 e) 0.3336 28. If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is less than 0.88? a) 0.2019 b) 0.2981 c) 0.5300 d) 0.7019 e) 0.7899 Homework #3 29. If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89? a) 0.1064 b) 0.2700 c) 0.3936 d) 0.6064 e) 0.9000 30. Suppose 40% of all college students have a computer at home and a sample of 64 is taken. What is the probability that more than 30 of those in the sample have a computer at home? a) 0.3686 b) 0.1314 c) 0.8686 d) 0.6314 e) 0.1343 31. Suppose 40% of all college students have a computer at home and a sample of 100 is taken. What is the probability that more than 50 of those in the sample have a computer at home? a) 0.4793 b) 0.9793 c) 0.0207 d) 0.5207 e) 0.6754 32. In an instant lottery, your chance of winning is 0.1. If you play the lottery 100 times and outcomes are independent, the probability that you win at least 15 percent of the time is a) 0.4933 b) 0.5000 Maho Sonmez maho.sonmez@utsa.edu 5 MS1023 Business Statistics with Computer Applications c) 0.1500 d) 0.0478 e) 0.9213 33. Suppose 40% of all college students have a computer at home and a sample of 100 students is taken. The mean of the sampling distribution of p is a) 0.4 b) 0.04 c) 40 d) 0.004 e) 4 34. Suppose 40% of all college students have a computer at home and a sample of 100 is taken. The standard deviation of the sampling distribution of p is a) 4.89 b) 0.0489 c) 0.24 d) 24 e) 0.4 35. If a company employs 3,500 people and if a random sample of 175 of these employees has been taken by systematic sampling, what is the value of k? a) 3500 b) 175 c) 200 d) 5 e) 20 36. If a company employs 3,500 people and if a random sample of 175 of these employees has been taken by systematic sampling, the researcher would start the sample selection between what two values? Homework #3 b) 0 and 175 c) 0 and 20 d) 0 and 3500 e) 20 and 175 37. A random sample of size 81 is drawn from a population with a standard deviation of 12. If only 18% of the time a sample mean greater than 300 is obtained, what is the mean of the population? a) 298.77 b) 301.23 c) 289.77 d) 278.97 e) 277.98 38. Suppose a population proportion is .40, and 80% of the time when you draw a random sample from this population you get a sample proportion of .35 or more. How large a sample were you taking? a) 60 b) 86 c) 76 d) 67 e) 68 A Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent business trip. Nineteen percent responded that it was for an internal company visit. Suppose 950 business travelers are randomly selected. Answer questions 39-41 based on the above information. 39. What is the probability that more than 25% of the business travelers say that the a) 175 and 3500 Maho Sonmez maho.sonmez@utsa.edu 6 MS1023 Business Statistics with Computer Applications reason for their most recent business trip was an internal company visit? a) 0.9999 b) 0.0000 c) 1.0000 d) 0.0100 e) 0.1000 Homework #3 42. If the population variance is $525, what is the probability of getting a sample mean of $110 or larger? a) 0.2500 b) 0.5000 c) 1.0000 d) 0.7500 e) 0.9500 40. What is the probability that between 15% and 20% of the business travelers say that the reason for their most recent business trip was an internal company visit? 43. If the population variance is $525, what is the probability of getting a sample mean larger than $135 per hour? a) 0.4992 b) 0.1140 c) 0.2852 d) 0.7844 e) 0.7852 a) 0.4932 b) 0.5000 c) 0.9932 d) 0.0068 e) 0.5068 41. What is the probability that between 133 and 171 of the business travelers say that the reason for their most recent business trip was an internal company visit? 44. If the population variance is $525, what is the probability of getting a sample mean of between $120 and $130 per hour? a) 0.49997 b) 0.21477 c) 0.2852 d) 0.78517 e) 0.7852 Suppose the average client charge per hour for out-of-court work by lawyers in the state of Iowa is $125. Suppose further that a random telephone sample of 32 lawyers in Iowa is taken and that the sample average charge per hour for out-of-court work is $110. Answer the questions 42-45 based on the above information. Maho Sonmez maho.sonmez@utsa.edu a) 0.3907 b) 0.8907 c) 0.0000 d) 0.1093 e) 0.7814 Questions 45-50 are based on the below information. The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be in each of the following? 7 MS1023 Business Statistics with Computer Applications 45. More than 59 pounds _________. a) 0.1003 b) 0.3997 c) 0.6003 d) 0.8997 e) 0.0003 46. More than 54 pounds _________. a) 0.4484 b) 0.9484 c) 0.0516 d) 0.8968 e) 0.5516 47. Between 56 and 58 pounds ________. a) 0.1772 b) 0.2580 c) 0.0808 d) 0.4352 e) 0.5648 48. Less than 55 pounds ________. a) 0.3531 b) 0.6469 c) 0.8531 d) 0.0668 e) 0.1469 49. Less than 51 pounds ________. a) 0.4996 b) 0.5004 c) 0.0004 d) 0.9996 e) 0.9992 50. Between 52 and 53 pounds ________. a) 0.4974 Maho Sonmez maho.sonmez@utsa.edu Homework #3 b) 0.0110 c) 0.4864 d) 0.9838 e) 0.0162 Chp. 8: Questions 51-100. 51. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using _______. a) a point estimate b) a range estimate c) a statistical parameter d) an interval estimate e) an exact estimate 52. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 45 randomly selected walk-in customers, and calculated that their mean waiting time was 15 minutes. If Brian concludes that the average waiting time for all walk-in customers is 15 minutes, he is using a ________. a) a range estimate b) a statistical parameter c) an interval estimate d) a point estimate e) an exact estimate 53. The z value associated with a two-sided 90% confidence interval is _______. a) 1.28 b) 1.645 c) 1.96 8 MS1023 Business Statistics with Computer Applications d) 2.575 e) 2.33 54. The z value associated with a two-sided 95% confidence interval is _______. a) 1.28 b) 1.645 c) 1.96 d) 2.575 e) 2.33 55. The z value associated with a two-sided 80% confidence interval is _______. a) 1.645 b) 1.28 c) 0.84 d) 0.29 e) 2.00 56. The z value associated with a two-sided 88% confidence interval is _______. a) 1.28 b) 1.55 c) 1.17 d) 0.88 e) 1.90 57. The z value associated with a two-sided 99% confidence interval is _______. a) 1.28 b) 1.645 c) 1.96 d) 2.575 e) 2.33 58. Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 99% confidence interval to estimate the population mean is _______. a) 94.08 to 101.92 b) 92.85 to 103.15 Maho Sonmez maho.sonmez@utsa.edu Homework #3 c) 97.35 to 98.65 d) 93.34 to 102.66 e) 90.20 to 105.00 59. Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 95% confidence interval for the population mean of waiting times is ________. a) 14.02 to 15.98 b) 7.16 to 22.84 c) 14.06 to 15.94 d) 8.42 to 21.58 e) 19.80 to 23.65 60. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 92% confidence interval for the population mean of training times is ________. a) 16.250 to 33.750 b) 24.300 to 25.710 c) 17.950 to 32.050 d) 24.125 to 25.875 e) 24.450 to 27.320 61. The table t value associated with the upper 5% of the t distribution and 12 degrees of freedom is _______. a) 2.1788 b) 1.7823 9 MS1023 Business Statistics with Computer Applications c) 1.3562 d) 3.0545 e) 1.7959 62. The table t value associated with the upper 2.5% of the t distribution and 26 degrees of freedom is _______. a) 1.7056 b) 2.0518 c) 2.7787 d) 2.0555 e) 1.7033 63. The table t value associated with the upper 10% of the t distribution and 23 degrees of freedom is _______. a) 1.3195 b) 1.7139 c) 2.4999 d) 1.3178 e) 1.7109 64. A researcher is interested in estimating the mean value for a population. She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32. She decides to construct a 98% confidence interval to estimate the mean. The degrees of freedom associated with this problem are _______. a) 18 b) 17 c) 16 d) 15 e) 20 65. A researcher is interested in estimating the mean value for a population. She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32. She decides to construct a 98% confidence interval to estimate the Maho Sonmez maho.sonmez@utsa.edu Homework #3 mean. The table t value associated with this problem is _______. a) 2.1199 b) 1.7459 c) 3.6862 d) 2.5669 e) 2.5835 66. A researcher is interested in estimating the mean value for a population. She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32. She decides to construct a 98% confidence interval to estimate the mean. The interval is _______. a) 204.08 to 243.92 b) 203.5 to 244.5 c) 203.332 to 244.668 d) 203.95 to 244.05 e) 204.07 to 245.04 67. Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. a) 63.37 to 86.63 b) 61.60 to 88.41 c) 71.77 to 78.23 d) 71.28 to 78.72 e) 79.86 to 81.28 68. A researcher wants to estimate the proportion of the population which possesses a given characteristic. A random sample of size 800 is taken resulting in 360 items which possess the characteristic. The point estimate for this population proportion is _______. 10 MS1023 Business Statistics with Computer Applications a) 0.55 b) 0.45 c) 0.35 d) 0.65 e) 0.70 69. A random sample of 225 items from a population results in 60% possessing a given characteristic. Using this information, the researcher constructs a 99% confidence interval to estimate the population proportion. The resulting confidence interval is _______. a) 0.54 to 0.66 b) 0.59 to 0.61 c) 0.57 to 0.63 d) 0.52 to 0.68 e) 0.68 to 0.76 70. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The point estimate for this population proportion is _______. a) 0.150 b) 0.300 c) 0.182 d) 0.667 e) 0.786 71. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 90% confidence interval for the population proportion is _________. a) 0.10847 to 0.19153 b) 0.15300 to 0.24700 c) 0.09126 to 0.20874 Maho Sonmez maho.sonmez@utsa.edu Homework #3 d) 0.14521 to 0.25514 e) 0.25514 to 0.26521 72. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 95% confidence interval for the population proportion is _________. a) 0.10847 to 0.19153 b) 0.15300 to 0.24700 c) 0.09126 to 0.20874 d) 0.10051 to 0.19949 e) 0.19921 to 0.20101 73. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 98% confidence interval for the population proportion is _________. a) 0.10847 to 0.19153 b) 0.15300 to 0.24700 c) 0.09126 to 0.20874 d) 0.14521 to 0.25514 e) 0.25514 to 0.26521 74. A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The range of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least _______. a) 44 b) 62 c) 216 d) 692 e) 700 11 MS1023 Business Statistics with Computer Applications 75. A study is going to be conducted in which a population mean will be estimated using a 92% confidence interval. The estimate needs to be within 12 of the actual population mean. The population variance is estimated to be around 2500. The necessary sample size should be at least _______. a) 15 b) 47 c) 54 d) 638 e) 700 76. In estimating the sample size necessary to estimate p, if there is no good approximation for the value of p available, the value of ____ should be used as an estimate of p in the formula. a) 0.10 b) 0.50 c) 0.40 d) 1.96 e) 2.00 77. A researcher wants to estimate the population proportion with a 95% level of confidence. He estimates from previous studies that the population proportion is no more than .30. The researcher wants the estimate to have an error of no more than .03. The necessary sample size is at least _______. Homework #3 which prefer the new packages; she will accept a 0.05 error. Previous studies indicate that new packaging has an approximately 70% acceptance rate. The sample size should be at least _______. a) 27 b) 59 c) 323 d) 427 e) 500 79. A researcher wants to estimate the population proportion with a 90% level of confidence. She estimates from previous studies that the population proportion is no more than .30. The researcher wants the estimate to have an error of no more than .02. The necessary sample size is at least _______. a) 29 b) 47 c) 298 d) 1421 e) 1500 80. A study will be conducted to estimate the population proportion. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least _______. a) 27 b) 188 c) 211 d) 897 e) 900 a) 1036 b) 160 c) 41 d) 259 e) 289 78. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She plans to use a 95% confidence interval estimate of the proportion of households 81. A study is going to be conducted in which a mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval. The estimate needs to be within 2 hours of Maho Sonmez maho.sonmez@utsa.edu 12 MS1023 Business Statistics with Computer Applications the actual population mean. The population standard deviation is estimated to be around 25. The necessary sample size should be at least _______. a) 100 b) 21 c) 923 d) 35 e) 423 82. If the population data is normally distributed and its standard deviation, , is known, interval estimates for the population mean must be determined using z-values regardless of the sample size, n. a) True b) False 83. Assumptions underlying the use of tstatistic in sample-based estimation are that the population is normally distributed and population standard deviation is unknown. a) False b) True 84. In determining the interval estimates for a population proportion using the sample proportion, it is appropriate to use the values from a t-distribution rather than the zdistribution. a) True b) False 85. A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. What is the point estimate of ? a) 70 b) 49 c) 90.4 d) 88.76 Maho Sonmez maho.sonmez@utsa.edu Homework #3 e) 92.04 86. A random sample of size 70 is taken from a population that has a variance of 49. The sample mean is 90.4. A 94% condence interval for is ___________. a) 88.76 to 92.04 b) 88.25 to 92.56 c) 79.39 to 101.4 d) 88.83 to 91.97 e) 89.02 to 91.78 87. The average total dollar purchase at a convenience store is less than that at a supermarket. Despite smaller-ticket purchases, convenience stores can still be protable because of the size of operation, volume of business, and the markup. A researcher is interested in estimating the average purchase amount for convenience stores in suburban Long Island. To do so, she randomly sampled 24 purchases from several convenience stores in suburban Long Island and tabulated the amounts to the nearest dollar (shown below). $2 $11 $8 $7 $9 $3 $5 $4 $2 $1 $10 $8 $14 $7 $6 $3 $7 $2 $4 $1 $3 $6 $8 $4 Assume that the population standard deviation is 3.23 and the population is normally distributed. Using the above data, a 90% condence interval for the population average amount of purchases is ____________. a) 4.54 to 6.71 b) 4.495 to 6.76 c) 4.44 to 6.81 d) 4.49 to 6.76 e) 4.26 to 6.99 13 MS1023 Business Statistics with Computer Applications Homework #3 88. A meat-processing company in the Midwest produces and markets a package of eight small sausage sandwiches. The product is nationally distributed, and the company is interested in knowing the average retail price charged for this item in stores across the country. The company cannot justify a national census to generate this information. Based on the company information system's list of all retailers who carry the product, a researcher for the company contacts 36 of these retailers and ascertains the selling prices for the product. 90. Some fast-food chains offer a lowerpriced combination meal in an effort to attract budget-conscious customers. One chain test-marketed a burger, fries, and a drink combination for $1.71. The weekly sales volume for these meals was impressive. Suppose the chain wants to estimate the average amount its customers spent on a meal at their restaurant while this combination offer was in effect. An analyst gathers data from 28 randomly selected customers. The following data represent the sample meal totals. $2.23 $2.16 $2.12 $2.01 $1.99 $2.23 $3.21 $5.02 $3.26 $3.73 $7.62 $2.11 $2.31 $2.07 $2.24 $1.87 $2.10 $2.12 $1.98 $2.17 $2.18 $2.09 $2.08 $2.20 $2.17 $2.30 $2.18 $2.22 $2.05 $2.17 $2.14 $2.29 $2.32 $2.15 $2.16 $2.10 $1.82 $2.19 $2.02 $2.19 $2.26 Use the above price data and assume a population standard deviation of 0.113. A 92% condence interval to estimate this price is ___________. a) 2.11 to 2.18 b) 2.10 to 2.17 c) 2.09 to 2.19 d) 2.11 to 2.17 e) 2.10 to 2.18 89. A random sample of 15 items is taken, producing a sample mean of 2.364 with a sample variance of .81.Assume x is normally distributed and construct a 98% condence interval for the population mean. The 98% confidence interval is _______. a) 2.320 to 2.408 b) 2.303 to 2.425 c) 1.815 to 2.913 d) 1.790 to 2.937 e) 2.300 to 2.428 Maho Sonmez maho.sonmez@utsa.edu $5.40 $4.20 $3.80 $4.08 $4.83 $3.50 $1.25 $5.46 $5.47 $8.42 $4.39 $7.64 $9.87 $4.49 $9.10 $5.60 $3.28 $4.67 $5.19 $8.65 $5.57 $5.86 $5.82 Assume the amounts spent are normally distributed. These data were used to construct a 90% condence interval to estimate the population mean value, which is _______________. a) 4.69 to 5.98 b) 4.72 to 5.95 c) 4.55 to 6.12 d) 4.57 to 6.10 e) 4.68 to 5.99 91. What proportion of pizza restaurants that are primarily for walk-in business have a salad bar? Suppose that, in an effort to determine this gure, a random sample of 1,250 of these restaurants across the United States based on the Yellow Pages is called. If 997 of the restaurants sampled have a salad bar, what is the 98% condence interval for the population proportion? a) 0.76278 to 0.81642 14 MS1023 Business Statistics with Computer Applications b) 0.77368 to 0.82632 c) 0.77891 to 0.81629 d) 0.77533 to 0.81987 e) 0.77116 to 0.82404 92. What proportion of commercial airline pilots are more than 40 years of age? Suppose a researcher has access to a list of all pilots who are members of the Commercial Airline Pilots Association. If this list is used as a frame for the study, she can randomly select a sample of pilots, contact them, and ascertain their ages. From 89 of these pilots so selected, she learns that 48 are more than 40 years of age. Construct an 85% condence interval to estimate the population proportion of commercial airline pilots who are more than 40 years of age. The 85% confidence interval is _______. a) 0.37353 to 0.52534 b) 0.46327 to 0.61538 c) 0.43577 to 0.64288 d) 0.45242 to 0.62623 e) 0.47161 to 0.60704 93. A bank ofcer wants to determine the amount of the average total monthly deposits per customer at the bank. He believes an estimate of this average amount using a condence interval is sufcient. How large a sample should he take to be within $200 of the actual average with 99% condence? He assumes the standard deviation of total monthly deposits for all customers is about $1,000. a) 165 b) 166 c) 167 d) 168 e) 169 Maho Sonmez maho.sonmez@utsa.edu Homework #3 94. A group of investors wants to develop a chain of fast-food restaurants. In determining potential costs for each facility, they must consider, among other expenses, the average monthly electric bill. They decide to sample some fast-food restaurants currently operating to estimate the monthly cost of electricity. They want to be 90% condent of their results and want the error of the interval estimate to be no more than $100. They estimate that such bills range from $600 to $2,500. How large a sample should they take? a) 12 b) 13 c) 14 d) 15 e) 16 95. What proportion of secretaries of Fortune 500 companies has a personal computer at his or her workstation? You want to answer this question by conducting a random survey. How large a sample should you take if you want to be 95% condent of the results and you want the error of the condence interval to be no more than .05? Assume no one has any idea of what the proportion actually is. a) 384 b) 385 c) 386 d) 387 e) 388 96. Suppose you want to estimate the proportion of cars that are sport utility vehicles (SUVs) being driven in Kansas City, Missouri, at rush hour by standing on the corner of I-70 and I-470 and counting SUVs. You believe the gure is no higher 15 MS1023 Business Statistics with Computer Applications than .40. If you want the error of the condence interval to be no greater than .03, how many cars should you randomly sample? Use a 90% level of condence. a) 725 b) 724 c) 723 d) 722 e) 721 97. According to a survey by Topaz Enterprises, a travel auditing company, the average error by travel agents is $128. Suppose this gure was obtained from a random sample of 41 travel agents and the sample standard deviation is $21. Compute a 98% condence interval for the national average error based on these sample results. Assume the travel agent errors are normally distributed in the population. How wide is the interval? a) 120.46 to 135.54 b) 120.16 to 135.84 c) 120.37 to 135.63 d) 122.48 to 133.52 e) 120.05 to 135.95 According to a survey by Runzheimer International, the average cost of a fast-food meal (quarter-pound cheeseburger, large fries, medium soft drink, excluding taxes) in Seattle is $4.82. Suppose this gure was based on a sample of 27 different establishments and the standard deviation was $0.37. Assume the costs of a fast-food meal in Seattle are normally distributed. Homework #3 98. What is the 95% condence interval for the population mean cost for all fast-food meals in Seattle? a) 4.08 to 5.56 b) 4.68 to 4.96 c) 4.67 to 4.97 d) 4.70 to 4.94 e) 4.69 to 4.94 99. Using the confidence interval as a guide, is it likely that the population mean is really $4.50? Why or why not? a) Yes, because $4.5 is inside the interval. b) Yes, because $4.5 is outside the interval. c) No, because $4.5 is inside the interval. d) No, because $4.5 is outside the interval. e) None of the above. 100. A regional survey of 561 companies asked the vice president of operations how satised he or she was with the software support received from the computer staff of the company. Suppose 187 of the 561 vice presidents said they were satised. What is the 99% condence interval for the proportion of the population of vice presidents who would have said they were satised with the software support if a census had been taken? a) 0.2821 to 0.3846 b) 0.2943 to 0.3723 c) 0.3006 to 0.3661 d) 0.2985 to 0.3682 e) 0.2959 to 0.3708 Answer questions 98-99 based on the above information. Maho Sonmez maho.sonmez@utsa.edu 16