Deck 7: Introduction to Sampling Distributions

Question 1

The sample mean is a parameter.

Answer 1

False

Question 2

Sampling error is the difference between the population value and the sample statistic.

Answer 2

True

Question 3

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.

Answer 3

False

Question 4

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.

Question 5

Taking a larger sample size will always result in less sampling error but costs more money and takes more time.

Question 6

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.

Question 7

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

Question 8

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

Question 9

The actual mean fill volume for all bottles of a soft drink product that were filled on a Tuesday is 11.998 ounces.A sample of 64 bottles was randomly selected and the sample mean fill volume was 12.004 ounces.Based upon this information,the sampling error is .006 ounces.

Question 10

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

Question 11

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

Question 12

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

Question 13

Recently the State Fish and Game planted several thousand tagged fish in a local river.The mean length of these fish,which constitute a population,is 12.6 inches.Yesterday,fishermen caught 100 of these tagged fish.You could expect that the mean length for these fish would be 12.6 inches as well since they come from the population.

Question 14

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.

Question 15

The size of the sampling error that comes from a random sample depends on both the variation in the population and the size of the sample being selected.

Question 16

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.

Question 17

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

Question 18

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.

Question 19

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

Question 20

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.

Question 21

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.

Question 22

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.

Question 23

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

Question 24

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

Question 25

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.

Question 26

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

Question 27

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.

Question 28

The population of soft drink cans filled by a particular machine is known to be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .25 ounces.Given this information,the sampling distribution for a random sample of n = 25 cans will also be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .05 ounces.

Question 29

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.

Question 30

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.

Question 31

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

Question 32

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.

Question 33

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 sampling distribution would have a mean equal to the population mean,but the standard deviation of the sampling distribution will be one-sixth of the population standard deviation.

Question 34

A sampling distribution for a sample of n = 4 is normally distributed with a standard deviation equal to 5.Based on this information,the population standard deviation,σ ,is equal to 10 mph.

Question 35

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.

Question 36

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.

Question 37

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 equal to 2 or more.

Question 38

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

Question 39

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

Question 40

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

Question 41

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.Then,the probability that a single turn time selected at random from this population would exceed 20 minutes is approximately 0.2327.

Question 42

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 ounces.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 0.4141.

Question 43

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.

Question 44

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

Question 45

A measure computed from the entire population is called:

A)a statistic.
B)a mean.
C)a parameter.
D)a qualitative value.

Question 46

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.

Question 47

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.

Question 48

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.

Question 49

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

Question 50

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.

Question 51

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

Question 52

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.

Question 53

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

Question 54

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.

Question 55

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

Question 56

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.

Question 57

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.

Question 58

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.

Question 59

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

Question 60

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

Question 61

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

Question 62

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 inches.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.The quality analysts will compute the mean length for the sample.They want to establish limits on either side of the 6.00 inch mean so that the chance of the sample mean falling within the limits is 0.99.What should these limits be?

A)Approximately ± 0.13 inches
B)Within the approximate range of 5.87 inches to 6.13 inches
C)Within the range of about 4.71 inches to 7.29 inches
D)Approximately ± 1.29 inches

Question 63

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 gallons.Based on this information,if the department employee selects a random sample of n = 9 containers,what is the probability that the mean volume for the sample will be greater than 1.01 gallons?

A)0.3821
B)0.1179
C)0.6179
D)0.2358

Question 64

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 x 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.

Question 65

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)0.4772
B)0.0228
C)0.6346
D)0.9544

Question 66

The following values represent the population of home mortgage interest rates (in percents)being charged by the banks in a particular city: 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

Question 67

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 gallons.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 gallons,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.

Question 68

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.

Question 69

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: If a random sample of n = 3 homes were selected,what would be the highest possible positive sampling error?

A)6.0
B)3.0
C)0.5
D)2.5

Question 70

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.

Question 71

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: 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.

Question 72

A particular subdivision has 20 homes.The number of people living in each of these homes is listed as follows: Which of the following statements is true when comparing a random sample of size three homes selected from the population to a random sample of size 6 homes selected from the population?

A)The amount of sampling error that will exist between the sample mean and the population mean will be half for the larger sample.
B)The most extreme negative sampling error between x and μ is reduced by about 0.167 people.
C)We can expect that the larger sample will produce more sampling error due to the potential to make coding errors.
D)The sampling error that will result from the smaller sample will be less than what we would see from the larger sample.

Question 73

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

Question 74

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.

Question 75

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 gallons.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 gallons,the department will fine the dairy.Based on this information,what is the probability that the dairy will get fined even when its filling process is working correctly?

A)0.90
B)Approximately 0.3159
C)About 0.1841
D)Approximately 0.3821

Question 76

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.

Question 77

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.

Question 78

The following values represent the population of home mortgage interest rates (in percents)being charged by the banks in a particular city: Given this information,what is the most extreme amount of sampling error possible if a random sample of n = 4 banks is surveyed and the mean loan rate is calculated?

A)-0.55 percent
B)0.52 percent
C)1.08 percent
D)Can't be determined without more information.

Question 79

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.

Question 80

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 mean of the sampling distribution for if the sample size is n = 64?

A)80
B)10
C)Between 72 and 88
D)8