Q&A Hero

Q: A population with a mean of 1,250 and a standard deviation of 400 is known to be highly skewed to the right. If a random sample of 64 items is selected from the population, what is the probability that the sample mean will be less than 1,325? A) 0.8981 B) 0.8141 C) 0.7141 D) 0.9332

Q: Princess Cruises recently offered a 16-day voyage from Beijing to Bangkok during the time period from May to August. The announced price, excluding airfare, for a room with an ocean view or a balcony was listed as $3,475. Cruise fares usually are quite variable due to discounting by the cruise line and travel agents. A sample of 20 passengers who purchased this cruise paid the following amounts (in dollars): 3,559 3,005 3,389 3,505 3,605 3,545 3,529 3,709 3,229 3,419 3,439 3,375 3,349 3,559 3,419 3,569 3,559 3,575 3,449 3,119 Determine the sampling error for this sample. A) -$29.70 B) -$51.12 C) -$21.71 D) -$31.74

Q: Hillman Management Services manages apartment complexes in Tulsa, Oklahoma. They currently have 30 units available for rent. The monthly rental prices (in dollars) for this population of 30 units are: 455 690 450 495 550 780 800 395 500 405 675 550 490 495 700 995 650 550 400 750 600 780 650 905 415 600 600 780 575 750 What is the range of possible sampling error if a random sample of size n = 10 is selected? A) -174.21 to 191.12 B) -182.59 to 169.91 C) -164.33 to 178.67 D) -162.16 to 171.51

Q: A sample of 25 observations is taken to estimate a population proportion π. The sampling distribution of sample proportion p is: A) not normal since n < 30. B) approximately normal because is always normally distributed. C) approximately normal if np ≥ 5 and n(1 - p) ≥ 5. D) approximately normal if p approaches 0.50.

Q: A major shipping company has stated that 96 percent of all parcels are delivered on time. To check this, a random sample of n = 200 parcels were sampled. Of these, 184 arrived on time. If the company's claim is correct, what is the probability of 184 or fewer parcels arriving on time? A) About 0.0019 B) Nearly 0.24 C) Just over 0.98 D) About 0.4981

Q: A pharmaceutical company claims that only 5 percent of patients experience nausea when they take a particular drug. In a research study, n = 100 patients were given this drug and 8 experienced nausea. Assuming that the company's claim is true, what is the probability of 8 or more patients experiencing nausea? A) About 0.9162 B) About 0.0300 C) About 0.0838 D) About 0.4162

Q: According to an industry report, 26 percent of all households have at least one cell phone. Further, of those that do have a cell phone, the mean monthly bill is $55.90 with a standard deviation equal to $9.60. Recently, a random sample of 400 households was selected. Of these households, 88 indicated that they had cell phones. The mean bill for these 88 households was $57.00. What is the probability of getting 88 or fewer households with cell phones if the numbers provided by the industry report are correct? A) Approximately 0.0344 B) Nearly 0.4656 C) About 0.1345 D) Can't be determined without knowing the standard deviation

Q: In a recent report, it was stated that the proportion of employees who carpool to their work is 0.14 and that the standard deviation of the sampling proportion is 0.0259. However, the report did not indicate what the sample size was. What was the sample size? A) 100 B) 180 C) 460 D) Can't be determined without more information

Q: One of the leading dot-com companies has found that the proportion of customers who come into its Web site that actually makes a purchase is 0.045. The company plans to see whether this rate still holds by selecting a random sample of 200 hits on its Web site. Given that the 0.045 rate still applies, what is the standard deviation of the sampling distribution? A) Approximately 0.0147 B) About 0.0002 C) About 0.0354 D) Can't be determined without knowing the mean.

Q: A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error. As a quality control measure, the publisher periodically selects a random sample of n = 100 pages. Then, depending on the proportion of pages with errors, they either say nothing to the printer or they complain that the quality has slipped. Suppose the publisher wants no more than a .10 chance of mistakenly blaming the printer for poor quality, what should the cut-off proportion be? A) About 0.0279 B) Approximately 0.0779 C) About 0.0221 D) About 0.10

Q: A claim was recently made on national television that two of every three doctors recommend a particular pain killer. Suppose a random sample of n = 300 doctors revealed that 180 said that they would recommend the painkiller. If the TV claim is correct, what is the probability of 180 or fewer in the sample agreeing? A) 0.4929 B) 0.0049 C) 0.9929 D) 0.0142

Q: The Chamber of Commerce in a large Midwestern city has stated that 70 percent of all business owners in the city favor increasing the downtown parking fees. The city council has commissioned a random sample of n = 100 business owners. Of these, 63 said that they favor increasing the parking fees. What is the probability of 63 or fewer favoring the idea if the Chamber's claim is correct? A) Approximately 0.0630 B) About 0.4370 C) Nearly 0.20 D) About 0.9370

Q: Which of the following statements is true with respect to the sampling distribution of a proportion? A) An increase in the sample size will result in a reduction in the size of the standard deviation. B) As long as the sample size is sufficiently large, the sampling distribution will be approximately normal. C) The mean of the sampling distribution will equal the population proportion. D) All of the above are true.

Q: A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. For a sample of 49, the probability that the sample mean will be larger than 82 is: A) 0.5228 B) 0.9772 C) 0.4772 D) 0.0228

Q: According to the local real estate board, the average number of days that homes stay on the market before selling is 78.4 with a standard deviation equal to 11 days. A prospective seller selected a random sample of 36 homes from the multiple listing service. Above what value for the sample mean should 95 percent of all possible sample means fall? A) About 79.3 days B) About 64 days C) Approximately 75.4 days D) Can't be determined without knowing whether the population is normally distributed.

Q: The St. Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inch. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less the 2.9 inches? A) 0.4977 B) 0.0023 C) 0.9977 D) 0.9954

Q: The J.R. Simplot Company produces frozen French fries that are then sold to customers such as McDonald's. The "prime" line of fries has an average length of 6.00 inches with a standard deviation of 0.50 inch. To make sure that Simplot continues to meet the quality standard for "prime" fries, they plan to select a random sample of n = 100 fries each day. Yesterday, the sample mean was 6.05 inches. What is the probability that the mean would be 6.05 inches or more if they are meeting the quality standards? A) 0.2350 B) 0.3413 C) 0.9413 D) 0.1587

Q: Which of the following statements is not consistent with the Central Limit Theorem? A) The Central Limit Theorem applies without regard to the size of the sample. B) The Central Limit Theorem applies to non-normal distributions. C) The Central Limit Theorem indicates that the sampling distribution will be approximately normal when the sample size is sufficiently large. D) The Central Limit Theorem indicates that the mean of the sampling distribution will be equal to the population mean.

Q: A golf course in California has determined that the mean time it takes for a foursome to complete an 18 hole round of golf is 4 hours 35 minutes (275 minutes) with a standard deviation of 14 minutes. The time distribution is also thought to be approximately normal. Every month, the head pro at the course randomly selects a sample of 8 foursomes and monitors the time it takes them to play. Suppose the mean time that was observed for the sample last month was 4 hours 44 minutes (284 minutes). What is the probability of seeing a sample mean this high or higher? A) Approximately 0.4649 B) About 0.9649 C) Approximately 0.0351 D) About 0.9298

Q: A company has determined that the mean number of days it takes to collect on its accounts receivable is 36 with a standard deviation of 11 days. The company plans to select a random sample of n = 12 accounts and compute the sample mean. Which of the following statements holds true in this situation? A) There is no way to determine what the mean of the sampling distribution is without knowing the specific shape of the population. B) The sampling distribution will have the same distribution as the population, provided that the population is not normally distributed. C) The sampling error will be larger than if they had sampled n = 64 accounts. D) The sampling distribution may actually be approximately normally distributed depending on what the population distribution is.

Q: Suppose it is known that the income distribution in a particular region is right-skewed and bi-modal. If bank economists are interested in estimating the mean income, which of the following is true? A) Provided that the sample size is sufficiently large, the sampling distribution for will be approximately normal with a mean equal to the population mean that they wish to estimate. B) The sampling distribution will also be right-skewed for large sample sizes. C) The standard deviation of the sampling distribution for will be proportionally larger than the population standard deviation, depending on the size of the sample. D) The sampling distribution will be left-skewed.

Q: The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices, such as scales, are accurate so customers and businesses are not cheated. Periodically, employees of the department go to businesses and test their scales. For example, a dairy bottles milk in 1-gallon containers. Suppose that if the filling process is working correctly, the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon. The department's test process requires that they select a random sample of n = 9 containers. If the sample mean is less than 0.97 gallon, the department will fine the dairy. Based on this information, suppose that the dairy wants no more than a 0.05 chance of being fined, which of the following options exist if they can't alter the filling standard deviation? A) They can convince the state to decrease the sample size. B) They can change the mean fill level to approximately 1.025 gallons. C) They could lower the mean fill level to a level lower than 1 gallon. D) There is actually nothing that they can do if they can't modify the standard deviation.

Q: The Olsen Agricultural Company has determined that the weight of hay bales is normally distributed with a mean equal to 80 pounds and a standard deviation equal to 8 pounds. Based on this, what is the probability that the mean weight of the bales in a sample of n = 64 bales will be between 78 and 82 pounds?A) 0.4772B) 0.0228C) 0.6346D) 0.9544

Q: The monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00. If a statistical sample of n = 100 customers is selected at random, what is the probability that the mean bill for those sampled will exceed $75.00? A) -0.33 B) Approximately 0.63 C) About 1.00 D) 3.33

Q: If the monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00, which of the following would be the largest individual customer bill that you might expect to find? A) Approximately $811.00 B) About $195.00 C) Nearly $123.00 D) There is no way to determine this without more information.

Q: A particular subdivision has 20 homes. The number of people living in each of these homes is listed as follows: 2 4 7 3 4 2 4 5 2 3 5 4 6 3 4 2 2 1 4 3 If a sample of size n = 5 is selected, the largest possible sample mean is: A) 7 B) 6.5 C) 6 D) 5.4

Q: Which of the following statements is false? A) Increasing the sample size will always reduce the size of the sampling error when the sample mean is used to estimate the population mean. B) Increasing the sample size will reduce the potential for extreme sampling error. C) Sampling error can occur when differs from μ due to the fact that the sample was not a perfect reflection of the population. D) There is no way to prevent sampling error short of taking a census of the entire population.

Q: Suppose the mean of dogs a pet shop grooms each day is know to be 14.2 dogs. If a sample of n = 12 days is chosen and a total of 178 dogs are groomed during those 12 days, then the sampling error is: A) 163.8. B) about 0.63. C) about -0.63. D) -163.8.

Q: The impact on sampling of increasing the sample size is: A) the potential for extreme sampling error is reduced. B) the amount of sampling error is always reduced. C) the sample mean will always be closer to the population mean. D) There is no specific relationship between sample size and sampling error.

Q: The following values represent the population of home mortgage interest rates (in percents) being charged by the banks in a particular city: 6.9 7.5 6.5 7 7.3 6.8 6.5 7 7 7.2 7.5 7.8 6 7 Given this information, what would the sampling error be if a sample including the seven values in the top row were used to compute the sample mean? A) Approximately 6.93 B) About 0.56 C) Approximately -0.07 D) About 0.07

Q: A measure computed from the entire population is called: A) a statistic. B) a mean. C) a parameter. D) a qualitative value.

Q: When sampling from a population, the sample mean will: A) typically exceed the population mean. B) likely be different from the population mean. C) always be closer to the population mean as the sample size increases. D) likely be equal to the population mean if proper sampling techniques are employed.

Q: Regardless of the value of the population proportion, p, (with the obvious exceptions of p = 0 and p = 1) the sampling distribution for the sample proportion, will be approximately normally distributed providing that the sample size is large enough.

Q: If the standard error for the sampling distribution of a proportion is equal to 0.0327 and if the population proportion, p, is equal to .80, the sample size must be 150.

Q: In analyzing the sampling distribution of a proportion, doubling the sample size will cut the standard deviation of the sampling distribution in half.

Q: The makers of a particular type of candy have stated that 75 percent of their sacks of candy will contain 6 ounces or more of candy. A consumer group that studies such claims recently selected a random sample of 100 sacks of this candy. Of these, 70 sacks actually contained 6 ounces or more. The probability that 70 or fewer sacks would contain 6 ounces or less is approximately 0.1251.

Q: In a campaign speech, a candidate for governor stated that about 63 percent of the people in the state were in favor of spending additional money on higher education. After the speech, a polling agency surveyed a random sample of 400 people and found 234 people who favored more spending on higher education. Based on the candidate's statement, the probability of finding 234 or fewer is approximately 0.97.

Q: A random sample of 500 customers at a large retail store was selected. These customers were asked whether they had a positive experience the last time they shopped there. Only 50 customers said that they did not have a positive experience. Thus, the population parameter for proportion of customers who did have a positive experience is .90.

Q: In a particular city, the proportion of cars that would fail an air quality emissions test is thought to be 0.13. Given this, the probability that a random sample of n = 200 cars will have a sample proportion between 0.11 and 0.15 is approximately 0.60.

Q: In order to assume that the sampling distribution for a proportion is approximately normal, the population proportion must be very close to 0.50.

Q: Assume that n = 18 people are asked a yes/no survey question, and 6 people say "yes" while 12 people say "no." Based on this information the sample proportion can be assumed normally distributed.

Q: The size of the standard error of the sample proportion is dependent on the value of the population proportion and the closer the population proportion is to .50, the larger the standard error for a given sample size will be.

Q: Suppose it is known that 93 percent of all parts in an inventory of 18,900 parts are in workable order. If a sample of n = 100 parts were selected from the inventory, based on the concept of sampling distributions of proportions, it can be assumed that the sample proportion of workable parts will also be 0.93.

Q: A sample proportion can be assumed normally distributed if n ≥ 30.

Q: Regardless of population distribution, the sampling distribution for a random variable X will be approximately normally distributed.

Q: The Fallbrook Distributing Company has a soft drink bottling plant in Plano, Texas. Based on historical records, if its filling machine is working properly, the mean fill volume per can is 12.0 ounces with a standard deviation equal to 0.13 ounce. Further, the distribution of fill amounts is known to be normally distributed. The State of Texas has a department whose job it is to check on such consumer-related processes as soft drink filling. The idea is to protect the consumer. The department arrives at the Fallbrook plant once a month on an unscheduled day. When they arrive, they randomly select n = 4 cans and carefully measure the volume in each can. If any of these cans contains less than 11.85 ounces, the plant is shut down until a full inspection of the filling process is performed. Based on this information, the probability that the plant will get shut down if it is operating properly is approximately 0.1251.

Q: One of the nation's biggest regional airlines has tracked 4,000 landings and take-offs during the past month. Treating these data as the population of interest, the company found that the average time the planes spent on the ground (called the turn time) was 17.23 minutes with a standard deviation of 3.79 minutes. Further, they determined that the distribution of turn times is normally distributed. If a sample of size n = 16 turn times was selected at random from the population, the chances of the mean of this sample exceeding 20 minutes is 0.2327.

Q: The Dilmart Company has 8,000 parts in inventory. The mean dollar value of these parts is $10.79 with a standard deviation equal to $3.34. Suppose the inventory manager selected a random sample of n = 64 parts from the inventory and found a sample mean equal to $11.27. The probability of getting a sample mean at least as large as $11.27 is approximately 0.444.

Q: If a population is not normally distributed, then the sampling distribution for the mean also cannot be normally distributed.

Q: The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490. Based on this, if a sample of size n = 36 is selected, the highest sample mean that we would expect to see would be approximately $38,034.

Q: If you are sampling from a very large population, a doubling of the sample size will reduce the standard error of the sampling distribution by one-fourth.

Q: When a population is not normally distributed, the Central Limit Theorem states that a sufficiently large sample will result in the sample mean being normally distributed.

Q: One of the things that the Central Limit Theorem tells us is that about half of the sample means will be greater than the population mean and about half will be less.

Q: The Central Limit Theorem is of most use to decision makers when the population is known to be normally distributed.

Q: If a population standard deviation is 100, then the sampling distribution for will have a standard deviation that is less than 100 for all sample sizes greater than 2.

Q: The sampling distribution for is actually the distribution of possible sampling error for samples of a given size selected at random from the population.

Q: If a population is normally distributed, then the sampling distribution for the sample mean will always be normally distributed regardless of the sample size.

Q: The population mean of income for adults in a particular community is known to be $28,600. Given this information, the sampling distribution of values will be less than this depending on the size of the sample used in developing the sampling distribution.

Q: The mean of a sampling distribution would be equal to the mean of the population from which the sampling distribution is constructed.

Q: A sampling distribution for is the distribution of all possible sample means that could be computed from the possible samples of a given sample size.

Q: Although the concept of sampling distributions is an important concept in statistics, it is very unlikely that a decision maker will actually construct a sampling distribution in any practical business situation.

Q: A sampling distribution for a sample mean shows the distribution of the possible values for the sample mean for a given sample size from a population.

Q: A sampling distribution is the distribution of the individual values that are included in a sample from a population.

Q: Sampling error can be eliminated if the sample size is large enough.

Q: A major automobile manufacturer has developed a new model car that it claims will average 25 mpg on the highway. A random sample of fifty of these cars was tested and they averaged 24 mpg. This means that the claim made by the auto company is incorrect.

Q: It is very unlikely that a nonstatistical sample will ever provide less sampling error than a statistical sample of the same size.

Q: If it is desired that sampling error be reduced, one step that tends to work is to increase the sample size that is selected from the population.

Q: Sampling error can be eliminated if the sampling is done properly.

Q: Sampling error occurs when the population parameter and the sample statistic are different.

Q: Suppose the mean balance of checking accounts at Regions Bank is known to be $4320. A random sample of 10 accounts yields a total of $41,490. This means the sampling error is -$171.

Q: A simple random sample is selected in a manner such that each possible sample of a given size has an equal chance of being selected.

Q: An increase in sample size will tend to result in less sampling error.

Q: If a population mean is equal to 200, the sample mean for a random sample selected from the population is about as likely to be higher or lower than 200.

Q: A local bank has 1,400 checking account customers. Of these, 1,020 also have savings accounts. A sample of 400 checking account customers was selected from the bank of which 302 also had savings accounts. The sampling error in this situation is .0264.

Q: A larger sample size reduces the potential for large sampling error.

Q: A smaller sample might provide less sampling error than a larger sample from a given population.

Q: Suppose it is known that the mean purchase price for all homes sold last year in Blacksburg, Virginia was $203,455. Recently, two studies were done on home sales prices. In the first study, a random sample of 200 homes was selected from the population. In the second study, a random sample of 60 homes was selected. Based on this information, we know that the second study would contain more sampling errors than the first study due to the smaller sample size.

Q: If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is that the sample might be biased.

Q: If the mean age for all students that attend your university is 24.78 years, it would be reasonable to expect that the mean of a sample of students selected from that population would also equal 24.78 years as long at the sampling is done using sound statistical methods.

Q: The reason that a population mean and the mean of a random sample selected from that population might be different is that the sample mean is found by dividing by n-1 while the population mean is found by dividing by n.