IVC/Spring 2016/Econ 10/MGT 10/ Pehlivan/ Exam 2 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which of the following is not a condition of a discrete probability distribution? A) The probability of a success must exceed the probability of a failure. B) Each outcome in the distribution needs to be mutually exclusive with other outcomes in the distribution. C) The probability of each outcome, P(x), must be between 0 and 1 (inclusive). D) The sum of the probabilities for all the outcomes in the distribution needs to add up to 1. 1) 2) The table below shows the numbers of two- to five-bedroom houses in the Belmont neighborhood. 2) Number of Bedrooms 2 3 4 5 Frequency 7 35 56 27 What is the mean number of bedrooms in a house in this neighborhood? A) 2.80 B) 2.43 C) 4.06 D) 3.82 ESSAY. Write your answer in the space provided or on a separate sheet of paper. 3) The following table shows the number of used cars sold each day over the last 25 business days at Newark Motors. Number of Sold Cars 0 1 2 3 4 5 Frequency 6 2 5 3 7 2 Probability 0.24 0.08 0.20 0.12 0.28 0.08 What is the standard deviation for the number of cars sold per day? MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) According to LIMRA, 77% of husband-wife families with kids under 18 years old have life insurance. A random sample of six husband-wife families was selected. What is the probability that exactly four families have life insurance? A) 0.4832 B) 0.5215 C) 0.3735 D) 0.2789 4) 5) According to the Insurance Research Council, 14% of U.S. drivers are uninsured. A random sample of seven drivers was selected. What is the standard deviation of this distribution? A) 0.573 B) 0.918 C) 1.457 D) 0.319 5) 1 ESSAY. Write your answer in the space provided or on a separate sheet of paper. 6) Kobe Bryant, a professional basketball player in the NBA, has made 84% of his free throws during his career with the Los Angeles Lakers. Calculate the probability that Bryant will make exactly three of his next five free throws. TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 7) The Poisson distribution can be used to approximate the binomial distribution when the number of trials is greater than 20 and the probability of success is less than or equal to 0.05. 7) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 8) Assume that the number of pieces of junk mail per day that a person receives in their mail box follows the Poisson distribution and averages 4.3 pieces per day. What is the probability that this person will not receive any junk mail tomorrow? A) 0.1069 B) 0.0136 C) 0.1360 D) 0.0314 8) 9) Which of the following experiments does not generate a continuous random variable? A) recording the number of minutes a customer waits on hold for technical support B) recording the number of miles traveled between two locations C) counting the number of customers who enter a store during the business day D) measuring the number of ounces of soda in a bottle 9) 10) John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes. What is the probability that the commute time for a randomly selected day will be less than 18 minutes? A) 0.0778 B) 0.2236 C) 0.0436 D) 0.1271 10) 11) Costco installs automobile tires on a first-come first-serve basis. The total time a customer needs to wait for the installation to be completed follows the normal distribution with a mean time of 106.3 minutes and a standard deviation of 18.5 minutes. What is the probability that a randomly selected customer will wait between 80 and 95 minutes for his or her tires to be installed? A) 0.3455 B) 0.2960 C) 0.1931 D) 0.1245 11) 12) According to Pew Research Center, 71% of Internet users accessed video-sharing sites last month. A random sample of 50 Internet users was selected. Using the normal approximation to the binomial distribution, what is the probability that exactly 36 people from this sample access video-sharing sites? A) 0.4286 B) 0.2005 C) 0.1217 D) 0.3669 12) 13) According to Bureau of Labor Statistics, 26.0% of the total part-time workforce in the U.S. was between the ages of 25 and 34 during a recent month. A random sample of 90 part-time employees was selected during this quarter. Using the normal approximation to the binomial distribution, what is the probability that exactly 23 people from this sample were between the ages of 25 and 34? A) 0.2394 B) 0.0951 C) 0.1615 D) 0.0419 13) 2 TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 14) The mathematical expression that describes the shape of the uniform distribution is known as the continuous uniform probability density function. 14) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 15) The time that customers wait to be served at the delicatessen for a grocery store follows the uniform distribution between 0 and 7 minutes. What is the probability that a randomly selected customer will wait between 1 and 5 minutes at the deli? A) 0.4286 B) 0.1429 C) 0.2857 D) 0.5714 15) 16) Periodicity is present in the population when A) there is a pattern in the sample consistent with the value of k that is chosen in cluster sampling. B) the population can be divided into mutually exclusive groups. C) there is a pattern in the population consistent with the value of k that is chosen in systematic sampling. D) the population cannot be divided into mutually exclusive groups. 16) 17) Susan would like to conduct a survey of homeowners in the Meadowbrook neighborhood to get their opinions on proposed road modifications in the area. She would like to sample 50 homes using systematic sampling. There are a total of 200 homes in the Meadowbrook neighborhood. What value of k should Susan use? A) 200 B) 50 C) 4 D) 10 17) 18) A ________ sample is a sample in which every member of the population has an equal chance of being chosen. A) systematic B) probability C) stratified D) simple random 18) 19) Consider the following population which represents the number of pieces of junk mail that I received during the month of February. 19) Using the first row of data as a sample, the sampling error is ________. A) 0.00 B) -0.50 C) 0.75 D) 0.25 ESSAY. Write your answer in the space provided or on a separate sheet of paper. 20) According to the Labor Department, the average duration of unemployment for adults ages 20 to 24 was 34.6 weeks during a recent month. Assume that the standard deviation for this population is 10.2 weeks. A random sample of 36 adults in this age group was selected. What is the probability that the average duration of unemployment was between 31 and 35 weeks? 3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 21) Suppose the average math SAT score for students enrolled at Madison College is 507.3 with a standard deviation of 68.2. A random sample of 49 students has been selected. The standard error of the mean for this sample is ________. A) 7.1 B) 38.4 C) 10.4 D) 68.2 21) 22) A Florida neighborhood is comprised of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from this neighborhood was selected. The standard error of the proportion is ________. A) 0.0566 B) 0.0272 C) 0.0748 D) 0.0341 22) 23) A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online? A) 0.6361 B) 0.4692 C) 0.3266 D) 0.5418 23) 24) According to comScore, Facebook users spent an average of 432 minutes on the site during a recent month. Assume that this population has a standard deviation of 127 minutes. A random sample of 50 users was selected from this population. What is the probability that the average number of minutes on the site in the recent month was less than 410 minutes? A) 0.1112 B) 0.3384 C) 0.2806 D) 0.0643 24) 25) According to Eurostat, 55.2% of households in Italy have one child, the highest percentage in the Euro zone. A random sample of 160 Italian households was selected. The standard error of the proportion is ________. A) 0.0410 B) 0.0165 C) 0.0393 D) 0.0454 25) 26) Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. Using this sample, the point estimate for the proportion of households without land lines is ________. A) 0.25 B) 0.32 C) 0.53 D) 0.48 26) 27) Apple would like to estimate the web browsing battery life of the iPad. The following data represents the battery life, in hours, experienced by six users. 27) Using this sample, the point estimate for the age of cars sold for the first time is ________. A) 13.26 B) 9.68 C) 11.50 D) 10.19 28) The ________ represents the probability that any given confidence interval will not contain the true population mean. A) significance level B) confidence interval C) margin of error D) confidence level 4 28) ESSAY. Write your answer in the space provided or on a separate sheet of paper. 29) Tire Kingdom installs automobile tires on a first-come first-served basis. A random sample of 50 customers experienced an average wait time of 93.7 minutes. Assume that the standard deviation of total wait time for all customers is 20.6 minutes. Determine the 90% confidence interval for this sample. 30) An HP inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 270 pages. Assume that the standard deviation for this population is 16.5 pages. A random sample of 40 customers was surveyed about the number of pages they were able to print with their black ink cartridges. The sample average was 268.1 pages. Use a 95% confidence interval to test the validity of HP's claim. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 31) A random sample of 60 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The 98% confidence interval around this sample mean is ________. A) (45.4, 56.0) B) (47.6, 53.8) C) (48.9, 52.5) D) (49.8, 51.6) 31) 32) The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The critical value for a 95% confidence interval around this sample mean is ________. A) 2.060 B) 1.708 C) 2.056 D) 1.706 32) 33) The average natural gas bill for a random sample of 21 homes in the 19808 zip code during the month of March was $311.90 with a sample standard deviation of $51.60. The approximate standard error of the mean for this sample is ________. A) 14.74 B) 8.20 C) 11.27 D) 9.93 33) 34) The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with a 99% confidence interval and a margin of error within plus or minus $6. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is ________. A) 313 B) 284 C) 210 D) 239 34) 35) The federal government would like to estimate the proportion of families with no savings. A pilot sample of 60 families found that 18 had no savings. The total sample size needed to construct a 95% confidence interval for the proportion of families with no savings with a margin of error equal to 6% is ________. A) 225 B) 460 C) 397 D) 425 35) 36) Travelocity would like to test if the average roundtrip airfare between New York and London is less than $1,400. A Type II error would occur if Travelocity concludes that the average airfare is 36) _______________________________________________. A) $1,400 or more when, in reality, the average airfare is less than $1,400 B) not equal to $1,400 when, in reality, the average airfare is equal to $1,400 C) equal to $1,400 when, in reality, the average airfare is not equal $1,400 or more. D) less than $1,400 when, in reality, the average airfare is $1,400 or more 5 37) The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set = 0.05. The correct hypothesis statement for this hypothesis test would be _______________________. A) H0 : 12; H1 : < 12 B) H0 : = 12; H1 : 12 C) H0 : 12; H1 : > 12 37) D) H0 : x = 12; H1 : x 12 38) The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and = 0.01 is ________. A) 2.33 B) 2.96 C) 2.05 D) 2.575 38) ESSAY. Write your answer in the space provided or on a separate sheet of paper. 39) Hallmark would like to test the hypothesis that those celebrating Valentine's Day will spend more than an average of $125 on gifts. A random sample of 18 people celebrating Valentine's Day spent an average of $148.50 with a standard deviation of $34.90. Hallmark would like to set = 0.01. Use the critical value approach to test this hypothesis. 40) Historically, voter turnout for political elections in Texas have been reported to be 54%. You have been assigned by a polling company to test the hypothesis that voter turnout during the most recent election was higher than 54%. You have collected a random sample of 90 registered voters from this elections and found that 54 actually voted. Assume that the true proportion of voter turnout is 0.67. Calculate the probability of a Type II error using = 0.02. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 41) The federal government would like to test the hypothesis that the average age of men filing for Social Security is higher than the average age of women set using = 0.05 with the following data: Sample mean Sample size Population standard deviation Men 64.5 years 35 3.0 years 41) Women 63.6 years 39 3.5 years If Population 1 is defined as men and Population 2 is defined as women, the p-value for this hypothesis test would be ________. A) 0.0122 B) 0.1492 C) 0.0262 D) 0.1170 TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 42) Once we set the value for for a hypothesis test, the value for becomes fixed. 6 42) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 43) AT&T would like to test the hypothesis that the proportion of 18- to 34-year-old Americans that own a cell phone is less than the proportion of 35- to 49-year-old Americans. A random sample of 200 18- to 34-year-old Americans found that 126 owned a smartphone. A random sample of 175 35- to 49-year-old Americans found that 119 owned a smartphone. If Population 1 is defined as 18- to 34-year-old Americans and Population 2 is defined as 35- to 49-year-old Americans, the p-value for this hypothesis test is ________. A) 0.1562 B) 0.1025 C) 0.0026 D) 0.0087 43) 44) Entertainment Software Association would like to test if the average age of "gamers" (those that routinely play video games) is more than 30 years old. A random sample of 33 gamers was selected and their ages were recorded. Assume that the standard deviation for the population of the age of gamers is 4.7 years and the true population mean for the age of gamers is 31.2 years. Using = 0.02, beta equals ________. A) 0.2918 B) 0.7224 C) 0.1247 D) 0.0434 44) 45) The power of the hypothesis test is the probability of of A) incorrectly rejecting the null hypothesis. B) incorrectly rejecting the alternative hypothesis. C) correctly rejecting the alternative hypothesis. D) correctly rejecting the null hypothesis. 45) __________________________. ESSAY. Write your answer in the space provided or on a separate sheet of paper. 46) The local Chamber of Commerce would like to estimate the average price of 93 octane gasoline for Chester County. There are currently 86 gas stations operating in the county. A random sample of 15 stations had an average price of $4.20 per gallon and a standard deviation of $0.24 per gallon. Determine the 95% confidence interval for the average price per gallon of 93 octane gasoline in Chester County. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 47) Which of the following statements is true regarding z-scores for the normal probability distribution? A) z-scores are zero for values of x that are less than the distribution mean. B) z-scores are equal to 1.0 for values of x that are equal to the distribution mean. C) z-scores are positive for values of x that are less than the distribution mean. D) z-scores are negative for values of x that are less than the distribution mean. 47) ESSAY. Write your answer in the space provided or on a separate sheet of paper. 48) The average attendance for Division 1 Men's NCAA Basketball games in 2011 was 5,237. Assume that attendance to these games follows the normal probability distribution with a standard deviation of 1,650. What is the probability that a randomly selected game during this year had an attendance more than 3,000? 7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 49) A random sample of 60 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The standard error of the mean for this sample is ________. A) 1.07 B) 0.63 C) 1.34 D) 2.30 49) 50) "No shows" are the people with reservations who fail to arrive. The following table shows the number of no shows each day at a hotel over the last 125 business days. 50) Number of No Shows 0 1 2 3 4 Frequency 61 35 10 12 7 What is the probability that there will be more than one no show today? A) 0.205 B) 0.232 C) 0.113 8 D) 0.147